Let's solve the equation step-by-step and identify the correct missing steps.
We start with the given equation:
[tex]\[ 2x - 6 = 4(x + 2) \][/tex]
Step 1: Expand the right-hand side of the equation.
[tex]\[ 2x - 6 = 4x + 8 \][/tex]
Step 2: Rearrange the equation to move all [tex]\(x\)[/tex] terms to one side and constant terms to the other side.
Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[ 2x - 4x - 6 = 4x - 4x + 8 \][/tex]
Simplify:
[tex]\[ -2x - 6 = 8 \][/tex]
Step 3: Continue to isolate [tex]\(x\)[/tex] by moving the constant term on the left side to the right side.
Add 6 to both sides:
[tex]\[ -2x - 6 + 6 = 8 + 6 \][/tex]
Simplify:
[tex]\[ -2x = 14 \][/tex]
Step 4: Solve for [tex]\(x\)[/tex] by dividing both sides by -2.
[tex]\[ x = \frac{14}{-2} \][/tex]
[tex]\[ x = -7 \][/tex]
So, the solution to the equation is [tex]\( x = -7 \)[/tex].
Given the options, the required steps to complete the equation are:
c. The subtraction of the [tex]\(4x\)[/tex] term from one side to move the [tex]\(x\)[/tex] to one side and the addition of 6 to the other side of the equation so [tex]\(x\)[/tex] is on one side and the other variable is on the other side of the equal sign.
This accurately describes the steps needed to isolate [tex]\(x\)[/tex] on one side of the equation.
