What is |5x+1/2 |-3<9 ?

The solution to |5x+1/2 |-3<9 is -5/2 <x< 23/10

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|5x+1/2 |-3<9

5 x + \frac{1}{2} - 3 < 9

- \frac{5}{2} < x < \frac{23}{10}

Interval Notation

(- \frac{5}{2}, \frac{23}{10})

Decimal Notation

- 2.5 < x < 2.3

Solution steps

5 x + \frac{1}{2} - 3 < 9

Move

3

to the right side

5 x + \frac{1}{2} < 12

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 12 < 5 x + \frac{1}{2} < 12

5 x + \frac{1}{2} > - 12 and 5 x + \frac{1}{2} < 12

x > - \frac{5}{2} and x < \frac{23}{10}

Merge Overlapping Intervals

- \frac{5}{2} < x < \frac{23}{10}

1 1^{\frac{1}{3}} \cdot 12 1^{\frac{1}{3}}

x^{2} - 4 + 3

- 5 (20 x) = 100

6 x^{2} - x - 15 = 0

n^{2} - 4