Question

Identify the steps followed to solve the equation 5−3(x+3)=11−8x
(5 points)
5−3x−9=11−8x
−3x−4=11−8x
5x−4=11
5x=15
x=3

Answer 1

Those steps are correct. Here they are with the justification for each:

1. 5 − 3(x + 3) = 11 − 8x
(original equation)

2. 5 − 3x − 9 = 11 − 8x
(distribute −3 across the parentheses)

3. −3x − 4 = 11 − 8x
(combine like terms: 5 − 9 = −4)

4. 5x − 4 = 11
(add 8x to both sides to move x-terms to the left: −3x + 8x = 5x)

5. 5x = 15
(add 4 to both sides)

6. x = 3
(divide both sides by 5)

Check: 5 − 3(3 + 3) = 5 − 18 = −13 and 11 − 8(3) = 11 − 24 = −13, so x = 3 is correct.