What is the solution to the equation below?4x+3(x−2)=8x−(6+x)This problem requires you to show your work.(1 point)Responses x=−4x is equal to negative 4infinite solutionsinfinite solutionsno solutionno solutionx=6 x is equal to 6

Answer 1

Let's solve the equation step by step:

The given equation is: \[ 4x + 3(x - 2) = 8x - (6 + x) \]

First, we will simplify both sides of the equation.

1. Distributing \(3\) on the left side: \[ 4x + 3x - 6 = 8x - (6 + x) \] This simplifies to: \[ 4x + 3x - 6 = 8x - 6 - x \]

2. Simplifying both sides: The left side simplifies to: \[ 7x - 6 \] The right side simplifies to: \[ 8x - x - 6 = 7x - 6 \]

So now we have: \[ 7x - 6 = 7x - 6 \]

3. Notice that both sides are equal: \[ 7x - 6 = 7x - 6 \]

This indicates that the equation is true for all values of \(x\). Therefore, we conclude that there are infinite solutions to the equation.

So, the correct response is: infinite solutions.