Question

-2(1/2) +2x <=4x/5 <=4/3+2x
Can anyone pls solve this​

Answer 1

SOLUTION

TO SOLVE

The inequality

$\displaystyle \sf{ - 2 \frac{1}{2} + 2x \leqslant \frac{4x}{5} \leqslant \frac{4}{3} + 2x \: \: \: , \: \: x \in \: W }$

EVALUATION

Here the given inequality is

$\displaystyle \sf{ - 2 \frac{1}{2} + 2x \leqslant \frac{4x}{5} \leqslant \frac{4}{3} + 2x \:}$

We solve the inequality as below

$\displaystyle \sf{ - 2 \frac{1}{2} + 2x \leqslant \frac{4x}{5} \leqslant \frac{4}{3} + 2x \:}$

$\displaystyle \sf{ \implies \: - \frac{5}{2} + 2x \leqslant \frac{4x}{5} \leqslant \frac{4}{3} + 2x \:}$

$\displaystyle \sf{ \implies \: - \frac{5}{2} + 2x - 2x \leqslant \frac{4x}{5} - 2x \leqslant \frac{4}{3} + 2x - 2x \:}$

$\displaystyle \sf{ \implies \: - \frac{5}{2} \leqslant - \frac{6x}{5} \leqslant \frac{4}{3}\:}$

$\displaystyle \sf{ \implies \: \bigg( - \frac{5}{2} \times 30 \bigg) \leqslant \bigg( - \frac{6x}{5} \times 30\bigg) \leqslant \bigg(\frac{4}{3} \times 30\bigg)\:}$

$\displaystyle \sf{ \implies \: - 75 \leqslant - 36x \leqslant 40\:}$

$\displaystyle \sf{ \implies \: - 40 \leqslant 36x \leqslant 75\:}$

$\displaystyle \sf{ \implies \: - \frac{10}{9} \leqslant x \leqslant \frac{25}{12} \:}$

Since x ∈ W where W is the whole number set

So x = 0 , 1 , 2

Hence the required solution set is

S = { 0 , 1 , 2 }

Number line : Number line is referred to the attachment . On the number A , B , C represents the numbers 0 , 1 , 2 respectively

FINAL ANSWER

Hence the required solution set is

S = { 0 , 1 , 2 }

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