Absolute Value Inequalities Calculator

FAQs

How do you solve inequalities with absolute value? To solve inequalities with absolute value, follow these general steps:

1. Isolate the absolute value expression on one side of the inequality.
2. Set up two cases by removing the absolute value and considering both positive and negative expressions.
3. Solve each case separately and find the solutions.
4. Combine the solutions based on the original inequality type (e.g., <, >, ≤, or ≥) to get the final solution.

What is absolute value and inequalities examples? Absolute value represents the distance of a number from zero on the number line, and it is always positive or zero. Examples of absolute value: |3| = 3, |-5| = 5. Examples of absolute value inequalities: |x| < 5, |2x + 1| ≥ 7.

What are the 3 steps to solve absolute value inequalities? The three steps to solve absolute value inequalities are:

1. Isolate the absolute value expression on one side of the inequality.
2. Set up two cases: One with the expression inside the absolute value as positive and the other as negative.
3. Solve each case separately and combine the solutions based on the original inequality type.

When the absolute value inequalities are greater than a negative number? When the absolute value inequalities are greater than a negative number (|x| > -a), the solution is always all real numbers since any value of x will satisfy the inequality. The absolute value of any number is always non-negative.

What is the rule for absolute value? The rule for absolute value is that the absolute value of a number is always non-negative. It is equal to the number itself if the number is positive or zero, and it is equal to the negative of the number if the number is negative.

What are the rules for absolute value equations? The rules for absolute value equations are:

1. |x| = a has two solutions: x = a and x = -a.
2. |x| = 0 has one solution: x = 0.

What are 3 examples of inequalities?

1. 2x + 3 < 7
2. -3y ≥ 9
3. 5z + 2 ≤ 12

What are 2 examples of inequalities?

1. x + 2 > 5
2. 3y - 1 < 10

What are the rules for inequalities? The rules for inequalities are similar to solving equations, with one exception: When multiplying or dividing both sides by a negative number, the inequality sign flips.

What is the easiest way to solve absolute value equations? The easiest way to solve absolute value equations is by setting up two cases, one with the expression inside the absolute value as positive and the other as negative, and then solving for the variable in each case.

What is the first step to solve absolute value inequalities? The first step to solve absolute value inequalities is to isolate the absolute value expression on one side of the inequality.

How to solve absolute value equations and inequalities by graphing? To solve absolute value equations and inequalities by graphing, plot the graph of both sides of the equation or inequality on the number line. The points where the graphs intersect represent the solutions.

What are the two types of absolute value inequalities? The two types of absolute value inequalities are "less than" (|x| < a) and "greater than" (|x| > a) inequalities.

What's the golden rule about inequalities and negatives? The golden rule about inequalities and negatives is that when you multiply or divide both sides of an inequality by a negative number, the inequality sign flips direction.

Why do inequalities flip when negative? Inequalities flip when multiplied or divided by a negative number because negative numbers are on the opposite side of zero compared to positive numbers. Multiplying or dividing by a negative changes the direction of the inequality.

What are the 4 steps to solving an absolute value equation? The four steps to solving an absolute value equation are:

1. Isolate the absolute value expression on one side of the equation.
2. Set up two cases: One with the expression inside the absolute value as positive and the other as negative.
3. Solve each case separately and find the solutions.
4. Check the solutions in the original equation.

Can you have a negative in absolute value? Yes, you can have a negative inside the absolute value. For example, |-3| = 3, as the absolute value of -3 is 3.

How do you know if an absolute value is positive or negative? The absolute value of a number is always positive or zero. The absolute value of a positive number remains the same, and the absolute value of a negative number becomes positive.

Is absolute value always positive? Yes, the absolute value of a number is always positive or zero.

What are the 4 rules of inequalities? The four rules of inequalities are:

1. Addition Property: If a < b, then a + c < b + c.
2. Subtraction Property: If a < b, then a - c < b - c.
3. Multiplication Property: If a < b and c > 0, then ac < bc. If a < b and c < 0, then ac > bc.
4. Division Property: If a < b and c > 0, then a/c < b/c. If a < b and c < 0, then a/c > b/c.

What is the formula of inequality? The formula of an inequality is similar to that of an equation, but it uses inequality symbols (<, >, ≤, ≥) instead of an equal sign (=).

How do you know if an equation is an inequality? An equation contains an equal sign (=), whereas an inequality contains inequality symbols (<, >, ≤, ≥) to show that two expressions are not necessarily equal.

How do you write a simple inequality? A simple inequality can be written as follows:

1. x < 5
2. y > -3

How do you explain inequalities in math? Inequalities in math compare two expressions to show their relationship, such as less than, greater than, less than or equal to, or greater than or equal to.

How do you write and solve inequalities? To write and solve inequalities, first, write the inequality using inequality symbols (<, >, ≤, ≥) to compare the expressions. Then, solve for the variable to find the valid range of values that satisfy the inequality.

What are the 5 types of inequalities in math? The five types of inequalities in math are:

1. Less than (<)
2. Greater than (>)
3. Less than or equal to (≤)
4. Greater than or equal to (≥)
5. Not equal to (≠)

What is the order of solving inequalities? The order of solving inequalities is similar to solving equations:

1. Simplify both sides.
2. Get all variable terms on one side and constants on the other side.
3. Isolate the variable on one side.
4. Check the solutions.

What is the golden rule for solving equations and inequalities? The golden rule for solving equations and inequalities is to perform the same operation on both sides to maintain the balance of the equation or inequality.

How do you find the absolute value for dummies? To find the absolute value of a number, remove the negative sign (if any) to get the positive value.

How to do absolute value step by step? To find the absolute value of a number x:

1. If x is positive, the absolute value is x itself.
2. If x is negative, the absolute value is -x.

What is an example of an absolute value equation? An example of an absolute value equation is |2x - 5| = 7.

Why do you solve for two answers when solving an absolute value inequality? When solving an absolute value inequality, you solve for two answers because there are two possible solutions when the absolute value expression can be both positive and negative.

What is an absolute value inequality with no solution? An absolute value inequality with no solution occurs when the inequality is impossible to satisfy, such as |x| < -2. There is no value of x that makes this inequality true.

What is always your last step of solving equations with absolute value? The last step of solving equations with absolute value is to check the solutions in the original equation to ensure they are valid.

How do you solve absolute value inequalities with two variables? To solve absolute value inequalities with two variables, follow the same steps as with one variable: isolate the absolute value expression and set up two cases.

How to solve an absolute value equation with variables on both sides? To solve an absolute value equation with variables on both sides, isolate the absolute value expression and set up two cases by removing the absolute value.

How do you write an absolute value inequality from a word problem? To write an absolute value inequality from a word problem, identify the information that represents the distance and set up an inequality with absolute value that expresses the conditions of the problem.

What are common mistakes in inequalities? Common mistakes in inequalities include forgetting to flip the inequality sign when multiplying or dividing by a negative number and missing the valid range of solutions.

What is the inequality paradox? The inequality paradox refers to situations where certain inequalities can lead to contradictory or nonsensical conclusions, highlighting the importance of correctly interpreting inequalities.

How do you solve two-step inequalities with negative numbers? To solve two-step inequalities with negative numbers, apply the same rules as in regular two-step inequalities, paying attention to the sign changes when multiplying or dividing by negative numbers.

Does multiplying negatives make positive? Yes, multiplying two negative numbers results in a positive product.

What is the rule for negative inequalities? When you multiply or divide both sides of an inequality by a negative number, the inequality sign flips direction.

When should you flip an inequality? You should flip an inequality when you multiply or divide both sides by a negative number.

Why does absolute value exist? Absolute value exists to measure the distance of a number from zero on the number line. It always provides a non-negative value.

How do you graph inequalities? To graph inequalities, first, plot the boundary line based on the equality symbol. Then, shade the region that satisfies the inequality based on the inequality symbol.

Can absolute value equal zero? Yes, the absolute value of zero is zero, as |0| = 0.

How do you solve absolute value inequalities? To solve absolute value inequalities, isolate the absolute value expression, set up two cases (one positive and one negative), and find the solutions for each case. Then, combine the solutions based on the inequality type.

Can an absolute value inequality equal a negative? No, an absolute value inequality cannot equal a negative value since absolute value is always non-negative.

How do you solve absolute value equations with negatives? To solve absolute value equations with negatives, isolate the absolute value expression and consider both positive and negative cases while solving.

What are the rules of absolute value? The rules of absolute value are:

1. |x| ≥ 0 (absolute value is non-negative)
2. |x| = x if x is non-negative, and |x| = -x if x is negative.

What happens when there is a negative in front of an absolute value? When there is a negative in front of an absolute value, it indicates that the expression inside the absolute value should be multiplied by -1 before evaluating the absolute value.

What happens when an absolute value is greater than a negative number? When an absolute value is greater than a negative number (|x| > -a), it implies that the absolute value is always greater than zero, so the solution is all real numbers.

Is the absolute value of a negative number always its opposite? Yes, the absolute value of a negative number is always its opposite. For example, |-(-5)| = |5| = 5.

Why the absolute value of a number is never negative? The absolute value of a number is never negative because it represents the distance of the number from zero on the number line, which is always a non-negative value.

Do you do absolute value first? Yes, when solving equations or inequalities involving absolute value, you typically isolate the absolute value expression first.

How do you write an absolute value equation from a number line? To write an absolute value equation from a number line, find the values of x that satisfy the condition on the number line and set up the equation accordingly.

How do you find absolute value? To find the absolute value of a number x:

1. If x is positive or zero, the absolute value is x itself.
2. If x is negative, the absolute value is -x.

How do you write an absolute value function? An absolute value function is written as f(x) = |x|, which means that the output of the function is the absolute value of the input x.

What is the absolute value of −4? The absolute value of -4 is 4, as |-4| = 4.

What is the absolute value of negative 8? The absolute value of -8 is 8, as |-8| = 8.

What is the absolute value of negative 6? The absolute value of -6 is 6, as |-6| = 6.

What are the 3 steps to solving an inequality? The three steps to solving an inequality are:

1. Simplify both sides of the inequality.
2. Get all variable terms on one side and constants on the other side.
3. Isolate the variable on one side.

What are 3 ways to solve inequalities? Three ways to solve inequalities are:

1. Algebraic manipulation: Using addition, subtraction, multiplication, and division to isolate the variable.
2. Graphical method: Plotting the inequality on a number line and shading the region that satisfies the inequality.
3. Numerical approach: Testing values to find which ones satisfy the inequality.

What are the 4 rules of inequalities? The four rules of inequalities are:

1. Addition Property: If a < b, then a + c < b + c.
2. Subtraction Property: If a < b, then a - c < b - c.
3. Multiplication Property: If a < b and c > 0, then ac < bc. If a < b and c < 0, then ac > bc.
4. Division Property: If a < b and c > 0, then a/c < b/c. If a < b and c < 0, then a/c > b/c.

How do you solve inequalities in 7th grade? In 7th grade, you solve inequalities by applying the basic rules of inequalities (addition, subtraction, multiplication, and division) to isolate the variable and find the solution set.

How do you tell if a value is a solution for an inequality? To determine if a value is a solution for an inequality, substitute the value into the inequality and see if it makes the inequality true.

What are examples of inequality equations? Examples of inequality equations are:

1. 3x + 2 < 10
2. 2y - 5 ≥ 7
3. -4z ≤ -12

What are 3 examples of inequalities?

1. x + 3 < 8
2. 2y - 5 > 10
3. -3z ≤ 9

How do you write and solve an inequality? To write and solve an inequality, express the relationship between two expressions using inequality symbols (<, >, ≤, ≥) and find the range of values that satisfy the inequality.

How do you identify inequalities? Inequalities are identified by the presence of inequality symbols (<, >, ≤, ≥) between two expressions, indicating their relationship.

What are the 5 types of inequalities in math? The five types of inequalities in math are:

1. Less than (<)
2. Greater than (>)
3. Less than or equal to (≤)
4. Greater than or equal to (≥)
5. Not equal to (≠)

What are the 4 steps to solving inequalities? The four steps to solving inequalities are:

1. Simplify both sides of the inequality.
2. Get all variable terms on one side and constants on the other side.
3. Isolate the variable on one side.
4. Write the solution set and represent it graphically if necessary.

How do you solve linear inequalities step by step? To solve linear inequalities step by step:

1. Simplify both sides of the inequality.
2. Get all variable terms on one side and constants on the other side.
3. Isolate the variable on one side.
4. Write the solution set and represent it graphically if necessary.

What are the 4 inequality signs? The four inequality signs are:

1. Less than (<)
2. Greater than (>)
3. Less than or equal to (≤)
4. Greater than or equal to (≥)

What are the basic rules of inequalities? The basic rules of inequalities include addition, subtraction, multiplication, and division to solve and manipulate inequalities.

What is the golden rule for solving inequalities? The golden rule for solving inequalities is to maintain the inequality sign direction when performing operations on both sides.

What is the most important rule to remember when solving inequalities? The most important rule to remember when solving inequalities is to flip the inequality sign direction when multiplying or dividing both sides by a negative number.

What are the 5 steps in solving rational inequality? The five steps in solving a rational inequality are:

1. Simplify the rational expression if possible.
2. Determine the critical points by setting the denominator equal to zero and solving for the variable.
3. Test intervals between the critical points to find where the rational expression changes sign.
4. Determine the sign of the expression in each interval and write the inequality.
5. Write the solution set and represent it graphically if necessary.

What is the absolute value of 25? The absolute value of 25 is 25, as |25| = 25.

What is an example of an absolute value inequality? An example of an absolute value inequality is |x - 3| < 5.

How do you find the absolute value for dummies? To find the absolute value of a number x:

1. If x is positive or zero, the absolute value is x itself.
2. If x is negative, the absolute value is -x.

What is an example of an absolute value equation? An example of an absolute value equation is |2x - 5| = 7.

Is absolute value always positive? Yes, the absolute value of a number is always positive or zero.

What is the absolute value of 12? The absolute value of 12 is 12, as |12| = 12.

Why is absolute value inequalities all real numbers? Absolute value inequalities are all real numbers because the absolute value of any real number is always non-negative, so there are no restrictions on the possible solutions.

Which inequality has no solution? An inequality with no solution is one where the conditions cannot be satisfied simultaneously. For example, x < 1 and x > 2 have no solution since there are no values of x that satisfy both conditions.

How many solutions are in absolute value equations? Absolute value equations can have one or two solutions.

What is the first step to solving absolute value equations? The first step to solving an absolute value equation is to isolate the absolute value expression on one side of the equation.

How do you write an absolute value inequality from a word problem? To write an absolute value inequality from a word problem, identify the information that represents the distance and set up an inequality with absolute value that expresses the conditions of the problem.

Do absolute value inequalities have two solutions? Yes, absolute value inequalities have two solutions because the absolute value expression can be both positive and negative.

How do you simplify absolute value expressions? To simplify absolute value expressions, evaluate the absolute value of the given number.

Can an absolute value be negative? No, an absolute value is always non-negative, which means it can be zero or positive but never negative.