Question

score: 0/2 penalty: none question solve for all values of x in simplest form. 7 + 2|3x + 3| = 11 answer attempt 1 out of 2 + additional solution - no solution x = submit a

Explanation:

Step1: Isolate the absolute - value term

Subtract 7 from both sides of the equation $7 + 2|3x + 3|=11$.
$2|3x + 3|=11 - 7$
$2|3x + 3|=4$
Divide both sides by 2: $|3x + 3| = 2$

Step2: Set up two equations

Since $|a|=b$ ($b\geq0$) implies $a = b$ or $a=-b$, we have:
$3x+3 = 2$ or $3x + 3=-2$

Step3: Solve the first equation

For $3x+3 = 2$, subtract 3 from both sides: $3x=2 - 3=-1$.
Divide both sides by 3: $x=-\frac{1}{3}$

Step4: Solve the second equation

For $3x + 3=-2$, subtract 3 from both sides: $3x=-2 - 3=-5$.
Divide both sides by 3: $x =-\frac{5}{3}$

Answer:

$x = -\frac{1}{3},x=- \frac{5}{3}$