Question

solve for v.
-7 = -4v + 7(v + 2)
simplify your answer as much as possible.

Explanation:

Step1: Expand the right - hand side

First, we use the distributive property \(a(b + c)=ab+ac\) to expand \(7(v + 2)\). So \(7(v + 2)=7v+14\). The equation becomes \(-7=-4v + 7v+14\).

Step2: Combine like terms

Combine the \(v\) terms on the right - hand side. \(-4v+7v = 3v\), so the equation is \(-7 = 3v+14\).

Step3: Isolate the variable term

Subtract 14 from both sides of the equation. \(-7-14=3v+14 - 14\). Calculating the left - hand side: \(-7-14=-21\), and the right - hand side becomes \(3v\). So we have \(-21 = 3v\).

Step4: Solve for \(v\)

Divide both sides of the equation by 3. \(\frac{-21}{3}=\frac{3v}{3}\). Simplifying, we get \(v=-7\).

Answer:

\(v = - 7\)