Solve the inequality.Express the solution set in interval notation. $| 5 x - 2 |

Question

Solve the inequality.Express the solution set in interval notation. $| 5 x - 2 | < 7$
A) $\quad \left( 1 , \frac { 9 } { 5 } \right)$
B) $\left( - 1 , \frac { 5 } { 9 } \right)$
C) $( 5,9 )$
D) $\left( - 1 , \frac { 9 } { 5 } \right)$
E) $\left( - \infty , - \frac { 9 } { 5 } \right) \cup ( - 1 , \infty )$

Quizplus · Accepted Answer

To solve the inequality, we will split it into two cases:

Case 1: $5x-2\geq 0$, which means $x\geq \frac{2}{5}$. In this case, the inequality becomes $5x-2< 7$, or $x< \frac{9}{5}$.

Case 2: $5x-2< 0$, which means $x< \frac{2}{5}$. In this case, the inequality becomes $-5x+2< 7$, or $x> -\frac{5}{9}$.

Putting these cases together, we get the solution set: $\left(-1,\frac{9}{5}\right)$. Therefore, the correct answer is D.

Solve the Inequality ∣5x−2∣<7| 5 x - 2 | < 7∣5x−2∣<7

Solve the Inequality $| 5 x - 2 | < 7$