Question

linear equations w/ distribution (lev 3)
score: 1/3 penalty: 1 off
question
solve for $x$:
$-8 + 8x=-5 + 3(3x + 4)$

Explanation:

Step1: Expand the right - hand side

Use the distributive property \(a(b + c)=ab+ac\). So, \(3(3x + 4)=3\times3x+3\times4 = 9x+12\). The equation becomes \(-8 + 8x=-5+9x + 12\).

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: \(-5 + 12=7\). The equation is \(-8 + 8x=9x+7\).

Step3: Move the \(x\) terms to one side

Subtract \(8x\) from both sides: \(-8+8x-8x=9x + 7-8x\), which simplifies to \(-8=x + 7\).

Step4: Solve for \(x\)

Subtract 7 from both sides: \(-8-7=x+7 - 7\). So, \(x=-15\).

Answer:

\(x=-15\)