Question

absolute value equations (level 1)
score: 0/2 penalty: none
question
solve for all values of x in simplest form.
5|10 + 3x| + 4 = 29
answer attempt 1 out of 2
additional solution no solution
x =

Explanation:

Step1: Isolate the absolute - value term

Subtract 4 from both sides of the equation $5|10 + 3x|+4 = 29$.
$5|10 + 3x|=29 - 4$
$5|10 + 3x|=25$

Step2: Solve for the absolute - value expression

Divide both sides by 5.
$|10 + 3x|=\frac{25}{5}$
$|10 + 3x| = 5$

Step3: Consider two cases

Case 1: $10+3x = 5$
Subtract 10 from both sides: $3x=5 - 10$
$3x=-5$
Divide both sides by 3: $x =-\frac{5}{3}$
Case 2: $10+3x=-5$
Subtract 10 from both sides: $3x=-5 - 10$
$3x=-15$
Divide both sides by 3: $x=-5$

Answer:

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