Solve the absolute value inequality. Write the solution in interval notation.
-$$| 2 x + 7 | + 7 6$$
A) $( - \infty , - 4 ) \cup ( - 3 , \infty )$
B) $( - 4 , - 3 )$
C) $( - \infty , \infty )$
D) \{ \}

Question

Solve the absolute value inequality. Write the solution in interval notation.
-$$| 2 x + 7 | + 7 > 6$$
A) $( - \infty , - 4 ) \cup ( - 3 , \infty )$
B) $( - 4 , - 3 )$
C) $( - \infty , \infty )$
D) \{ \}

Quizplus · Accepted Answer

First, simplify the inequality: $| 2x + 7 | + 7 > 6$ becomes $| 2x + 7 | > -1$. Since the absolute value of any real number is always greater than or equal to 0, and thus always greater than -1, the solution set includes all real numbers, which is represented by $( - \infty , \infty )$.

Solve the Absolute Value Inequality ∣2x+7∣+7>6| 2 x + 7 | + 7 > 6∣2x+7∣+7>6

Solve the Absolute Value Inequality $| 2 x + 7 | + 7 > 6$