What is |((3x))/(4-2)|<8 ?

The solution to |((3x))/(4-2)|<8 is -16/3 <x< 16/3

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|((3x))/(4-2)|<8

\frac{( 3 x )}{4 - 2} < 8

- \frac{16}{3} < x < \frac{16}{3}

Interval Notation

(- \frac{16}{3}, \frac{16}{3})

Decimal Notation

- 5.33333 \dots < x < 5.33333 \dots

Solution steps

\frac{3 x}{4 - 2} < 8

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 8 < \frac{3 x}{4 - 2} < 8

\frac{3 x}{4 - 2} > - 8 and \frac{3 x}{4 - 2} < 8

x > - \frac{16}{3} and x < \frac{16}{3}

Merge Overlapping Intervals

- \frac{16}{3} < x < \frac{16}{3}

∣ 19 + 3 x ∣ \geq 46

\frac{( x - 4 )}{5} < 4

x^{2} - ∣ 3 x + 2 ∣ + x \leq 0

∣ x - 11 ∣ + ∣ x + 2 ∣ \leq \frac{1}{4}

x^{2} - 4 > x^{2} - 4