What is |5x+1/2 |-4<8 ?

The solution to |5x+1/2 |-4<8 is -5/2 <x< 23/10

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|5x+1/2 |-4<8

5 x + \frac{1}{2} - 4 < 8

- \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} - 4 < 8

Move

4

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}

3 x - 2 = - 7

(- \frac{q ^{4}}{5})^{- 3}

3 + 3

3 x (x + 5) = 0

3 \leq x - 1 \leq 7