(2x+8)/6+8=x-4

2 min read Jun 16, 2024

Solving the Equation: (2x + 8)/6 + 8 = x - 4

This article will guide you through solving the equation (2x + 8)/6 + 8 = x - 4. We'll break down the steps and use clear explanations to make the process easy to follow.

Step 1: Simplify the Left Side

First, we need to simplify the left side of the equation. Let's start by getting rid of the fraction:

Multiply both sides by 6: This gives us 2x + 8 + 48 = 6x - 24
Combine like terms: 2x + 56 = 6x - 24

Step 2: Isolate the Variable

Now we need to get all the x terms on one side of the equation and all the constant terms on the other side.

Subtract 2x from both sides: This gives us 56 = 4x - 24
Add 24 to both sides: This gives us 80 = 4x

Step 3: Solve for x

The final step is to isolate x.

Divide both sides by 4: This gives us x = 20

Solution

Therefore, the solution to the equation (2x + 8)/6 + 8 = x - 4 is x = 20.

Verification

To verify our solution, we can substitute x = 20 back into the original equation and see if it holds true.

(2(20) + 8)/6 + 8 = 20 - 4
(40 + 8)/6 + 8 = 16
48/6 + 8 = 16
8 + 8 = 16
16 = 16

This confirms that our solution x = 20 is correct.