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

The solution to | 1/2 x+1/3 |<6 is -38/3 <x< 34/3

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

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

- \frac{38}{3} < x < \frac{34}{3}

Interval Notation

(- \frac{38}{3}, \frac{34}{3})

Decimal Notation

- 12.66666 \dots < x < 11.33333 \dots

Solution steps

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

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

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

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

x > - \frac{38}{3} and x < \frac{34}{3}

Merge Overlapping Intervals

- \frac{38}{3} < x < \frac{34}{3}

x^{2} + 8 x - 5 = 0

- x^{2} + 4 x

36 x^{2} - 2 = 79

6 (x - 7) - 7 (x - 6) = x + 6 - (x - 2)

4 x^{(2)} + 8 x - 1 = 0