What is |5x+1/2 |-2<5 ?

The solution to |5x+1/2 |-2<5 is -3/2 <x< 13/10

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|5x+1/2 |-2<5

5 x + \frac{1}{2} - 2 < 5

- \frac{3}{2} < x < \frac{13}{10}

Interval Notation

(- \frac{3}{2}, \frac{13}{10})

Decimal Notation

- 1.5 < x < 1.3

Solution steps

5 x + \frac{1}{2} - 2 < 5

Move

2

to the right side

5 x + \frac{1}{2} < 7

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 7 < 5 x + \frac{1}{2} < 7

5 x + \frac{1}{2} > - 7 and 5 x + \frac{1}{2} < 7

x > - \frac{3}{2} and x < \frac{13}{10}

Merge Overlapping Intervals

- \frac{3}{2} < x < \frac{13}{10}

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