Question

linear equations w/ distribution (lev 3)
score: 2/6 penalty: none
question
solve for ( x ):
( 3(-7x - 3) + 4x = -(x - 3) )
answer attempt 1 out of 2
( x = ) submit answer

Explanation:

Step1: Distribute the terms

First, we distribute the 3 on the left side and the -1 on the right side.
For the left side: \(3(-7x - 3)=3\times(-7x)+3\times(-3)= -21x - 9\)
For the right side: \(-(x - 3)=-x + 3\)
So the equation becomes: \(-21x - 9 + 4x=-x + 3\)

Step2: Combine like terms on the left

Combine the \(x\)-terms on the left side: \(-21x+4x=-17x\)
Now the equation is: \(-17x - 9=-x + 3\)

Step3: Add \(17x\) to both sides

To get all the \(x\)-terms on one side, we add \(17x\) to both sides:
\(-17x - 9+17x=-x + 3+17x\)
Simplifying both sides: \(-9 = 16x+3\)

Step4: Subtract 3 from both sides

Subtract 3 from both sides to isolate the term with \(x\):
\(-9 - 3=16x+3 - 3\)
Simplifying: \(-12 = 16x\)

Step5: Divide both sides by 16

Divide both sides by 16 to solve for \(x\):
\(x=\frac{-12}{16}\)
Simplify the fraction by dividing numerator and denominator by 4: \(x =-\frac{3}{4}\)

Answer:

\(-\frac{3}{4}\)