Question

7x - 8(-x + 7) = -16 + 7x

Explanation:

Step1: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), for \(-8(-x + 7)\), we have \(-8\times(-x)+(-8)\times7 = 8x-56\). So the original equation \(7x-8(-x + 7)=-16 + 7x\) becomes \(7x + 8x-56=-16 + 7x\).

Step2: Combine like terms on the left - hand side

Combine \(7x\) and \(8x\): \(7x+8x = 15x\), so the equation is \(15x-56=-16 + 7x\).

Step3: Subtract \(7x\) from both sides

\(15x-7x-56=-16 + 7x-7x\), which simplifies to \(8x-56=-16\).

Step4: Add 56 to both sides

\(8x-56 + 56=-16 + 56\), so \(8x=40\).

Step5: Divide both sides by 8

\(\frac{8x}{8}=\frac{40}{8}\), which gives \(x = 5\).

Answer:

\(x = 5\)