What is the answer to 44-2(3x+4)=-18x

Solving algebraic equations is a fundamental skill in mathematics, and the equation 44 – 2(3x + 4) = -18x is no exception. In this 1000-word blog post, we will delve into the step-by-step process of solving this equation, explore the principles of algebraic manipulation, and discuss the significance of equation solving in various fields.

What is the answer to 44-2(3x+4)=-18x

The solution to the equation 44 – 2(3x + 4) = -18x is x = -3. By following the steps of algebraic manipulation, we isolate the variable x and find that it equals -3, making the equation true. This solution satisfies the equation’s requirements and demonstrates the power of algebra in problem-solving.

Understanding the Equation

Let’s start by understanding the equation itself:

44 – 2(3x + 4) = -18x

This is a linear equation involving a single variable, x. Our goal is to find the value of x that makes this equation true.

Step-by-Step Solution

To solve this equation, we follow a series of steps:

Step 1: Distribute the 2 on the left side of the equation:

44 – 6x – 8 = -18x

Now, the equation becomes:

36 – 6x = -18x

Step 2: Isolate the x terms on one side of the equation:

To do this, we need to move all terms containing x to one side and constants to the other side.

36 + 18x = 6x

Step 3: Combine like terms:

36 + 18x – 6x = 0

12x = -36

Step 4: Solve for x by dividing both sides by 12:

(12x)/12 = (-36)/12

x = -3

Step 5: Check the solution:

We should always check our solution by plugging it back into the original equation to ensure it satisfies the equation.

44 – 2(3x + 4) = -18x

44 – 2(3(-3) + 4) = -18(-3)

44 – 2(-9 + 4) = 54

44 – 2(-5) = 54

44 + 10 = 54

54 = 54

The equation is satisfied, which means our solution, x = -3, is correct.

Significance of Equation Solving

Solving equations is a fundamental skill with practical applications in various fields:

1. Engineering: Engineers use equation solving to design structures, analyze systems, and optimize processes.
2. Physics: Equations are central to understanding the laws of the universe, from motion to electromagnetism.
3. Economics: Economic models and forecasts often involve solving equations to predict trends and make decisions.
4. Computer Science: Algorithms and programming frequently require solving equations to solve real-world problems.
5. Finance: Financial analysts use equations to calculate interest rates, investment returns, and risk assessments.

Conclusion

Solving equations is a vital mathematical skill that plays a significant role in many aspects of our lives. In the case of the equation 44 – 2(3x + 4) = -18x, we followed a step-by-step process to find the solution, x = -3. This solution allows us to satisfy the equation and demonstrates the power of algebraic manipulation in solving real-world problems and making informed decisions.