Question

solve for x.
-2(3x - 5) - 2x - 2 = -40

Explanation:

Step1: Distribute -2

First, we distribute the -2 across the terms inside the parentheses. Using the distributive property \(a(b - c)=ab - ac\), we have:
\(-2(3x - 5)=-2\times3x-2\times(-5)=-6x + 10\)
So the equation becomes \(-6x + 10-2x - 2=-40\)

Step2: Combine like terms

Next, we combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(-6x-2x=-8x\). For the constant terms: \(10 - 2 = 8\). So the equation simplifies to:
\(-8x+8=-40\)

Step3: Subtract 8 from both sides

We subtract 8 from both sides of the equation to isolate the term with \(x\).
\(-8x+8 - 8=-40 - 8\)
Which simplifies to:
\(-8x=-48\)

Step4: Divide by -8

Finally, we divide both sides of the equation by -8 to solve for \(x\).
\(\frac{-8x}{-8}=\frac{-48}{-8}\)
\(x = 6\)

Answer:

\(x = 6\)