What is |6x+1/2 |-4<3 ?

The solution to |6x+1/2 |-4<3 is -5/4 <x< 13/12

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|6x+1/2 |-4<3

6 x + \frac{1}{2} - 4 < 3

- \frac{5}{4} < x < \frac{13}{12}

Interval Notation

(- \frac{5}{4}, \frac{13}{12})

Decimal Notation

- 1.25 < x < 1.08333 \dots

Solution steps

6 x + \frac{1}{2} - 4 < 3

Move

4

to the right side

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

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 7 < 6 x + \frac{1}{2} < 7

6 x + \frac{1}{2} > - 7 and 6 x + \frac{1}{2} < 7

x > - \frac{5}{4} and x < \frac{13}{12}

Merge Overlapping Intervals

- \frac{5}{4} < x < \frac{13}{12}

\frac{( - 2 ) ^{4}}{4} - (- 2)^{2}

3 x - 8 < 13

(\frac{2}{3})^{9}

2 s + 2 \geq 10

0 = (x - 4)^{2} - 9