2x-1-x-2-lt-4-find-the-solution-set-

Question Number 110294 by bemath last updated on 28/Aug/20

∣ 2 x + 1 ∣ - ∣ x - 2 ∣ < 4

f i n d t h e s o l u t i o n s e t

Answered by Rio Michael last updated on 28/Aug/20

∣ 2 x + 1 ∣ = {\begin{cases} 2 x + 1, x ⩾ - \frac{1}{2} \\ - (2 x + 1), x < - \frac{1}{2} \end{cases}

∣ x - 2 ∣ = {\begin{cases} x - 2, x ⩾ 2 \\ - (x - 2), x < 2 \end{cases}

for x < - \frac{1}{2}, - (2 x + 1) - [- (x - 2)] < 4

\Rightarrow - 2 x - 1 + x - 2 < 4

\Rightarrow - x - 3 < 4 or x > - 7

for - \frac{1}{2} ⩽ x < 2, 2 x + 1 + x - 2 < 4

\Rightarrow 3 x - 1 < 4 or x < \frac{5}{3}

for x ⩾ 2, 2 x + 1 - (x - 2) < 4

\Rightarrow 2 x + 1 - x + 2 < 4

x < 1

x > - 7, x < \frac{5}{3} and x < 1

\Rightarrow - 7 < x < \frac{5}{3}

Commented by bemath last updated on 28/Aug/20

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