Question

linear equations w/ distribution (lev 3)
score: 2/3 penalty: 1 off
question
solve for x:
4x + 2(x - 1) + 4 = -4x

Explanation:

Step1: Expand the equation

$4x + 2(x - 1)+4=-4x$ becomes $4x+2x - 2 + 4=-4x$ by using the distributive property $a(b - c)=ab - ac$ where $a = 2$, $b=x$ and $c = 1$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side and the constant terms on the left - hand side, we get $(4x+2x)+(-2 + 4)=-4x$, which simplifies to $6x+2=-4x$.

Step3: Add $4x$ to both sides

$6x + 2+4x=-4x+4x$, resulting in $10x+2 = 0$.

Step4: Subtract 2 from both sides

$10x+2-2=0 - 2$, giving $10x=-2$.

Step5: Divide both sides by 10

$\frac{10x}{10}=\frac{-2}{10}$, so $x=-\frac{1}{5}$.

Answer:

$x =-\frac{1}{5}$