Question

spiraling - solving equations
solve for x. use the sketchpad to show your work.
4 = 4(2x + 8) + 6x
x =

Explanation:

Step1: Expand the right side

First, we use the distributive property \(a(b + c)=ab+ac\) to expand \(4(2x + 8)\). So \(4(2x+8)=4\times2x + 4\times8 = 8x+32\). The equation becomes \(4=8x + 32+6x\).

Step2: Combine like terms

Combine the \(x\)-terms on the right side. \(8x+6x = 14x\), so the equation is \(4=14x + 32\).

Step3: Subtract 32 from both sides

Subtract 32 from both sides of the equation to isolate the term with \(x\). \(4-32=14x+32 - 32\), which simplifies to \(- 28=14x\).

Step4: Divide both sides by 14

Divide both sides by 14 to solve for \(x\). \(\frac{-28}{14}=\frac{14x}{14}\), so \(x=- 2\).

Answer:

\(x = - 2\)