Solve the linear inequality. Express the solution in set-builder notation.
- $\frac { 5 } { 2 } x + 4 < \frac { 2 } { 5 }$

Question

Solve the linear inequality. Express the solution in set-builder notation. -$$\frac { 5 } { 2 } x + 4 < \frac { 2 } { 5 }$$ A) $\left\{ x \mid x < - \frac { 36 } { 25 } \right\}$ B) $\left\{ x \mid x > - \frac { 36 } { 25 } \right\}$ C) $\left\{ x \mid x > \frac { 2 } { 5 } \right\}$ D) $\left\{ x \mid x < \frac { 2 } { 5 } \right\}$

Quizplus · Accepted Answer

To solve the inequality $\frac { 5 } { 2 } x + 4 < \frac { 2 } { 5 }$, first subtract 4 from both sides to get $\frac { 5 } { 2 } x < \frac { 2 } { 5 } - 4$. Converting 4 to a fraction with a denominator of 5 gives $\frac { 5 } { 2 } x < \frac { 2 } { 5 } - \frac { 20 } { 5 }$, which simplifies to $\frac { 5 } { 2 } x < -\frac { 18 } { 5 }$. Multiplying both sides by $\frac { 2 } { 5 }$ to isolate x gives $x < -\frac { 36 } { 25 }$.

Solve the Linear Inequality 52x+4<25\frac { 5 } { 2 } x + 4 < \frac { 2 } { 5 }25​x+4<52​

Solve the Linear Inequality $\frac { 5 } { 2 } x + 4 < \frac { 2 } { 5 }$