Question

linear equations w/ distribution (lev 2)
score: 2/4 penalty: none
question
solve for x.
-3(-3x + 2) - 2x - 1 = -35

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b + c)=ab+ac\). For \(-3(-3x + 2)\), we have \((-3)\times(-3x)+(-3)\times2 = 9x-6\).
The equation becomes \(9x-6-2x - 1=-35\).

Step2: Combine like terms

Combine the \(x\) - terms (\(9x-2x = 7x\)) and the constant terms (\(-6-1=-7\)).
The equation is now \(7x-7=-35\).

Step3: Isolate the term with \(x\)

Add \(7\) to both sides of the equation. Using the addition property of equality \(a=b\Rightarrow a + c=b + c\), we get \(7x-7 + 7=-35 + 7\).
So, \(7x=-28\).

Step4: Solve for \(x\)

Divide both sides by \(7\) using the division property of equality \(a=b\Rightarrow\frac{a}{c}=\frac{b}{c}(c
eq0)\).
\(x=\frac{-28}{7}\).

Answer:

\(x=-4\)