Question

Solve the absolute value equation 6−2|3x+2|−9=−11
6
−
2
|
3
𝑥
+
2
|
−
9
=
−
11
.(1 point)
Responses

x=−2
𝑥
=
−
2
and x=23
𝑥
=
2
3
x equals negative 2 and x equals Start Fraction 2 over 3 End Fraction

x=−5
𝑥
=
−
5
and x=113
𝑥
=
11
3
x equals negative 5 and x equals Start Fraction 11 over 3 End Fraction

x=23
𝑥
=
2
3
x equals Start Fraction 2 over 3 End Fraction

no solution

Answer 1

Solve: 6 − 2|3x+2| − 9 = −11
Simplify: −3 − 2|3x+2| = −11 → −2|3x+2| = −8 → |3x+2| = 4
So 3x+2 = 4 → x = 2/3, or 3x+2 = −4 → x = −2.

Answer: x = −2 and x = 2/3.