Question

linear equations w/ distribution (lev 3)
score: 4/6 penalty: none
question
solve for ( x ):
( x - (5x + 3) - 3 = -(-x + 2) )
answer attempt 1 out of 2
( x = ) submit answer

Explanation:

Step1: Distribute the negative signs

First, we distribute the negative sign in \( -(5x + 3) \) and \( -(-x + 2) \).
For \( x - (5x + 3) - 3 \), distributing the negative sign gives \( x - 5x - 3 - 3 \).
For \( -(-x + 2) \), distributing the negative sign gives \( x - 2 \).
So the equation becomes:
\( x - 5x - 3 - 3 = x - 2 \)

Step2: Combine like terms on the left side

Combine the \( x \) terms and the constant terms on the left side.
The \( x \) terms: \( x - 5x = -4x \)
The constant terms: \( -3 - 3 = -6 \)
So the equation is now:
\( -4x - 6 = x - 2 \)

Step3: Move all \( x \) terms to one side and constants to the other

Subtract \( x \) from both sides:
\( -4x - x - 6 = x - x - 2 \)
\( -5x - 6 = -2 \)
Then add 6 to both sides:
\( -5x - 6 + 6 = -2 + 6 \)
\( -5x = 4 \)

Step4: Solve for \( x \)

Divide both sides by -5:
\( x = \frac{4}{-5} = -\frac{4}{5} \)

Answer:

\( x = -\frac{4}{5} \)