Solve the absolute value inequality. Write the solution in interval notation.
-$$| 2 b - 23 | \geq - 15$$
A) $[ 4,19 ]$
B) { }
C) $( - \infty , 4 ] \cup [ 19 , \infty )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

Absolute value inequalities of the form $|x| \geq a$, where $a$ is a non-positive number (in this case, $-15$), are always true for all real numbers because the absolute value is always non-negative. Thus, the solution is all real numbers, represented by $( - \infty , \infty )$.

Solve the Absolute Value Inequality ∣2b−23∣≥−15| 2 b - 23 | \geq - 15∣2b−23∣≥−15

Solve the Absolute Value Inequality $| 2 b - 23 | \geq - 15$