Question
Solve the following inequalities and represent the solution set on a number line:
$-3<-\frac{1}{2}-\frac{2 x}{3}<\frac{5}{6}, x \in R$.
$-3<-\frac{1}{2}-\frac{2 x}{3}<\frac{5}{6}, x \in R$.
✓
Answer
$-3<-\frac{1}{2}-\frac{2 x}{3}<\frac{5}{6}$
⇒ -18 < -3 - 4x ≤ 5
⇒ -15 < - 4x ≤ 8
$\Rightarrow-2 \leq x<\frac{15}{4}$
⇒ -18 < -3 - 4x ≤ 5
⇒ -15 < - 4x ≤ 8
$\Rightarrow-2 \leq x<\frac{15}{4}$
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