Question

solve for x.
$-4(x + 2) - x + 2 = -21$

Explanation:

Step1: Distribute -4

First, we distribute the -4 across the terms inside the parentheses \((x + 2)\). Using the distributive property \(a(b + c)=ab+ac\), we get:
\(-4(x + 2)=-4x-8\)
So the equation becomes \(-4x - 8 - x + 2=-21\)

Step2: Combine like terms

Next, we combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(-4x - x=-5x\). For the constant terms: \(-8 + 2=-6\).
So the equation simplifies to \(-5x-6=-21\)

Step3: Add 6 to both sides

To isolate the term with \(x\), we add 6 to both sides of the equation.
\(-5x-6 + 6=-21 + 6\)
Simplifying both sides gives \(-5x=-15\)

Step4: Divide by -5

Finally, we divide both sides of the equation by -5 to solve for \(x\).
\(\frac{-5x}{-5}=\frac{-15}{-5}\)
This simplifies to \(x = 3\)

Answer:

\(x = 3\)