Question

question
solve for x.
4(-x + 5) - 3x - 2 = 11
answer attempt 1 out of 2
x =

Explanation:

Step1: Expand the left side

First, we expand \(4(-x + 5)\) using the distributive property \(a(b + c)=ab+ac\). So, \(4(-x + 5)=4\times(-x)+4\times5=-4x + 20\). Then the original equation \(4(-x + 5)-3x - 2 = 11\) becomes \(-4x+20 - 3x-2 = 11\).

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms on the left side. For the \(x\)-terms: \(-4x-3x=-7x\). For the constant terms: \(20 - 2 = 18\). So the equation simplifies to \(-7x+18 = 11\).

Step3: Isolate the \(x\)-term

Subtract 18 from both sides of the equation. \(-7x+18-18 = 11 - 18\), which gives \(-7x=-7\).

Step4: Solve for \(x\)

Divide both sides by \(-7\). \(\frac{-7x}{-7}=\frac{-7}{-7}\), so \(x = 1\).

Answer:

\(x = 1\)