What is |7x+1/2 |-2<8 ?

The solution to |7x+1/2 |-2<8 is -3/2 <x< 19/14

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|7x+1/2 |-2<8

7 x + \frac{1}{2} - 2 < 8

- \frac{3}{2} < x < \frac{19}{14}

Interval Notation

(- \frac{3}{2}, \frac{19}{14})

Decimal Notation

- 1.5 < x < 1.35714 \dots

Solution steps

7 x + \frac{1}{2} - 2 < 8

Move

2

to the right side

7 x + \frac{1}{2} < 10

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 10 < 7 x + \frac{1}{2} < 10

7 x + \frac{1}{2} > - 10 and 7 x + \frac{1}{2} < 10

x > - \frac{3}{2} and x < \frac{19}{14}

Merge Overlapping Intervals

- \frac{3}{2} < x < \frac{19}{14}

x^{2} - 33 x + 125 = 0

(- 8 a^{5} b^{7})^{0}

- 15 = \frac{3}{7} b

0 = 2 d - 16

∣ 4 - x ∣ = ∣ 2 x + 1 ∣