Of course! Let's solve the equation step by step.
Given the equation:
[tex]\[ -2(x + 6) - 6 = 4(-1 - x) \][/tex]
Step 1: Distribute the constants inside the parentheses.
For the left-hand side:
[tex]\[ -2(x + 6) = -2 \cdot x + (-2) \cdot 6 = -2x - 12 \][/tex]
Substituting this back into the equation gives:
[tex]\[ -2x - 12 - 6 = 4(-1 - x) \][/tex]
For the right-hand side:
[tex]\[ 4(-1 - x) = 4 \cdot (-1) + 4 \cdot (-x) = -4 - 4x \][/tex]
Substituting this back into the equation gives:
[tex]\[ -2x - 12 - 6 = -4 - 4x \][/tex]
Step 2: Simplify both sides.
Combine like terms on the left-hand side:
[tex]\[ -2x - 18 = -4 - 4x \][/tex]
Step 3: Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constant terms to the other side.
Add [tex]\( 4x \)[/tex] to both sides:
[tex]\[ -2x + 4x - 18 = -4 - 4x + 4x \][/tex]
[tex]\[ 2x - 18 = -4 \][/tex]
Step 4: Isolate [tex]\( x \)[/tex].
Add 18 to both sides:
[tex]\[ 2x - 18 + 18 = -4 + 18 \][/tex]
[tex]\[ 2x = 14 \][/tex]
Divide both sides by 2:
[tex]\[ x = \frac{14}{2} \][/tex]
[tex]\[ x = 7 \][/tex]
Therefore, the solution is:
[tex]\[ x = 7 \][/tex]
