Question

solve for g. 14 = 4(-3g - 19) + 18g g =

Explanation:

Step1: Expand the right side

First, use the distributive property to expand \(4(-3g - 19)\). The distributive property states that \(a(b + c)=ab+ac\), so here \(a = 4\), \(b=-3g\), and \(c = - 19\). So we get \(4\times(-3g)+4\times(-19)=-12g-76\). Then the equation becomes \(14=-12g - 76+18g\).

Step2: Combine like terms

Combine the \(g\)-terms on the right side. \(-12g+18g = 6g\), so the equation is now \(14=6g - 76\).

Step3: Add 76 to both sides

To isolate the term with \(g\), add 76 to both sides of the equation. \(14 + 76=6g-76 + 76\), which simplifies to \(90 = 6g\).

Step4: Divide both sides by 6

Now, divide both sides by 6 to solve for \(g\). \(\frac{90}{6}=\frac{6g}{6}\), so \(g = 15\).

Answer:

\(15\)