Question

linear equations w/ distribution (lev 2)
score: 0/3 penalty: none
question
solve for x.
3(-4x - 5) + 5x + 4 = -4

Explanation:

Step1: Distribute the 3

First, we use the distributive property \( a(b + c)=ab+ac \) to expand \( 3(-4x - 5) \).
\( 3(-4x-5)=3\times(-4x)+3\times(-5)=-12x - 15 \)
So the equation becomes \( -12x-15 + 5x+4=-4 \)

Step2: Combine like terms

Combine the \( x \)-terms and the constant terms.
For the \( x \)-terms: \( -12x+5x=-7x \)
For the constant terms: \( -15 + 4=-11 \)
The equation now is \( -7x-11=-4 \)

Step3: Isolate the \( x \)-term

Add 11 to both sides of the equation to isolate the term with \( x \).
\( -7x-11 + 11=-4 + 11 \)
Simplifying both sides: \( -7x=7 \)

Step4: Solve for \( x \)

Divide both sides by -7 to solve for \( x \).
\( \frac{-7x}{-7}=\frac{7}{-7} \)
Simplifying gives \( x = - 1 \)

Answer:

\( x=-1 \)