How do you solve $- 3 < - \frac{1}{2} - \frac{2 x}{3} \leq \frac{5}{6}$ $-3< - \frac { 1} { 2} - \frac { 2x } { 3} \leq \frac { 5} { 6}$ ?

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How do you solve $- 3 < - \frac{1}{2} - \frac{2 x}{3} \leq \frac{5}{6}$ $-3< - \frac { 1} { 2} - \frac { 2x } { 3} \leq \frac { 5} { 6}$ ?

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Answer 1 · 2018-05-26T12:30:52

$- 2 \leq x < 3 \frac{3}{4}$ $-2<=x<3 3/4$

Explanation:

Multiply all by 6:
$- 3 \cdot 6 < \frac{- 1 \cdot 6}{2} - \frac{2 x \cdot 6}{3} \leq \frac{5 \cdot 6}{6}$ $-3*6<(-1*6)/2-(2x*6)/3<=(5*6)/6$
$- 18 < - 3 - 4 x \leq 5$ $-18<-3-4x<=5$

Add 3 to all:
$- 15 < - 4 x \leq 8$ $-15<-4x<=8$

Multiply all by -1:
$15 > 4 x \geq - 8$ $15>4x>=-8$
$- 8 \leq 4 x < 15$ $-8<=4x<15$

Divide all by 4:
$- 2 \leq x < \frac{15}{4}$ $-2<=x<15/4$
$- 2 \leq x < 3 \frac{3}{4}$ $-2<=x<3 3/4$

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How do you solve $- 3 < - \frac{1}{2} - \frac{2 x}{3} \leq \frac{5}{6}$ $-3< - \frac { 1} { 2} - \frac { 2x } { 3} \leq \frac { 5} { 6}$ ?

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How do you solve $- 3 < - \frac{1}{2} - \frac{2 x}{3} \leq \frac{5}{6}$ $-3< - \frac { 1} { 2} - \frac { 2x } { 3} \leq \frac { 5} { 6}$ ?