Question

solve the equation.
4(2 + 2x) = 7(x - 1)
select the correct choice below and fill in any answer boxes in your choice.
a. the solution set is { }. (type an integer or a simplified fraction )
b. there is no solution.

Explanation:

Step1: Expand both sides

Expand the left side: \(4(2 + 2x)=8 + 8x\). Expand the right side: \(7(x - 1)=7x - 7\). Now the equation is \(8 + 8x = 7x - 7\).

Step2: Isolate the variable \(x\)

Subtract \(7x\) from both sides: \(8 + 8x - 7x = 7x - 7 - 7x\), which simplifies to \(8 + x = -7\). Then subtract 8 from both sides: \(x = -7 - 8\).

Step3: Calculate the value of \(x\)

\(x = -15\).

Answer:

A. The solution set is \(\{-15\}\)