Question

Solve and represent on number line: $-2^{\frac{1}{2}} + 2x \leq ^ {\frac{4x}{5}} \leq ^ {\frac{4}{3}} + 2x, x$

Answer 1

Answer:

x ∈ [-5/6 , 25/16 ]

Step-by-step explanation:

The soluition of this inequality is obtained

by simplification.

$-2\frac{1}{2}+2x\leq\frac{4x}{5}\leq\frac{4}{3}+2x\\\\subtract \:throughout\: by\: 2x\\\\\frac{-5}{2}+2x-2x\leq\frac{4x}{5}-2x\leq\frac{4}{3}+2x-2x\\\\\frac{-5}{2}\leq\frac{-8x}{5}\leq\frac{4}{3}\\\\multiply \:throughout\: by -5/8\\\\(\frac{-5}{2})(\frac{-5}{8})\geq\frac{-8x}{5}(\frac{-5}{8})\geq\frac{4}{3}(\frac{-5}{8})\\\\\frac{25}{16}\geq\:x\:\geq\frac{-5}{6}$

x ∈ [-5/6 , 25/16 ]