Solve the absolute value inequality. Write the solution in interval notation.
-$$3 | x - 9 | + 9

Question

Solve the absolute value inequality. Write the solution in interval notation.
-$$3 | x - 9 | + 9 < 15$$
A) $( 1,17 )$
B) $( 7,11 )$
C) $( - \infty , 7 ) \cup ( 11 , \infty )$
D) $( - \infty , 1 ) \cup ( 17 , \infty )$

Quizplus · Accepted Answer

First, isolate the absolute value: $3 | x - 9 | < 6$. Divide by 3: $| x - 9 | < 2$. This gives two inequalities: $x - 9 < 2$ and $x - 9 > -2$. Solving these gives $x < 11$ and $x > 7$, so the solution is $(7, 11)$.

Solve the Absolute Value Inequality 3∣x−9∣+9<153 | x - 9 | + 9 < 153∣x−9∣+9<15

Solve the Absolute Value Inequality $3 | x - 9 | + 9 < 15$