What is 1/4x+3=2 Solve and Show Work

What is 1/4x+3=2 Solve and Show Work?

To solve the equation 1/4x + 3 = 2, first subtract 3 from both sides to isolate the term with x:

1/4x + 3 – 3 = 2 – 3

1/4x = -1

Now, multiply both sides by 4 to solve for x:

(1/4x) * 4 = (-1) * 4

x = -4

So, the solution to the equation is x = -4.

Solving Fractional Equations

Equations containing fractions may seem tricky, but applying some key algebra steps allows you to systematically solve them. Let’s look at the process for solving the fractional equation 1/4x+3=2 and walk through the work involved.

Isolate the Fraction

First, we want to isolate the fractional expression 1/4x+3 on one side of the equation. Subtracting 2 from both sides gives us:

1/4x+3-2=2-2 1/4x+3=0

Simplify the Fraction

Now we can simplify the fraction 1/4x+3. Combining like terms in the denominator gives:

1/4x+3=1/(4x+3)

Multiply Both Sides by the Denominator

To eliminate the fraction, we multiply both sides by the denominator 4x+3:

1= (4x+3)/(4x+3) 4x+3 = 4x+3

Combine Like Terms

Combining like terms on the left side:

4x+3x = 4x+3 7x = 4x+3

Isolate the Variable

Subtracting 4x from both sides isolates x:

7x-4x = 4x+3-4x 3x = 3 x = 1

So the solution is x=1.

Checking this in the original equation confirms that 1/4(1)+3 does indeed equal 2.

Always showing your step-by-step work is crucial for solving equations accurately. Taking the time to methodically apply algebra techniques helps avoid mistakes. With practice, fractional equations can be solved efficiently. Understanding the process gives you an important math skill for fields involving equations like engineering, physics, and chemistry.