Question

-4x + 51 = 2x + 7(x + 11)

Explanation:

Step1: Expand the right - hand side

We need to expand \(7(x + 11)\) using the distributive property \(a(b + c)=ab+ac\). So \(7(x + 11)=7x+77\). The equation becomes \(-4x + 51=2x+7x + 77\).

Step2: Combine like terms on the right - hand side

Combine \(2x\) and \(7x\) on the right - hand side. \(2x+7x = 9x\), so the equation is \(-4x + 51=9x+77\).

Step3: Move the \(x\) terms to one side

Add \(4x\) to both sides of the equation to get all the \(x\) terms on one side. \(-4x+4x + 51=9x + 4x+77\), which simplifies to \(51 = 13x+77\).

Step4: Move the constant terms to the other side

Subtract 77 from both sides. \(51-77=13x+77 - 77\), so \(-26 = 13x\).

Step5: Solve for \(x\)

Divide both sides by 13. \(\frac{-26}{13}=\frac{13x}{13}\), which gives \(x=- 2\).

Answer:

\(x = - 2\)