Question

$- \frac{1}{4} \leqslant \frac{1}{2} - \frac{x}{3} < 2$

Solve the Linear Inequality.​

Answer 1

Step-by-step explanation:

1st take left side

$\frac{ - 1}{4} \leqslant \frac{1}{2} - \frac{x}{3} \\ = > \frac{ - 1}{4} \leqslant \frac{3 - 2x}{6} \\ = > - 6 \leqslant 4(3 - 2x) \\ = > - 3 \leqslant 2(3 - 2x) = 6 - 4x \\ = > 6 - 4x \geqslant - 3 \\ = > 6 - 4x + 3 \geqslant 0 \\ = > - 4x + 9 \geqslant 0 \\ = > 4x - 9 \leqslant 0$

next come to 2nd part

$\frac{1}{2} - \frac{x}{3} < 2 \\ = > \frac{3 - 2x}{6} < 2 \\ = > 3 - 2x < 12 \\ = > 12 - 3 + 2x > 0 \\ = > 2x + 9 > 0$