What is 6|3x+5|<= 14 ?

The solution to 6|3x+5|<= 14 is -22/9 <= x<=-8/9

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6|3x+5|<= 14

6 ∣ 3 x + 5 ∣ \leq 14

- \frac{22}{9} \leq x \leq - \frac{8}{9}

Interval Notation

[- \frac{22}{9}, - \frac{8}{9}]

Decimal Notation

- 2.44444 \dots \leq x \leq - 0.88888 \dots

Solution steps

6 ∣ 3 x + 5 ∣ \leq 14

Divide both sides by

6

∣ 3 x + 5 ∣ \leq \frac{7}{3}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{7}{3} \leq 3 x + 5 \leq \frac{7}{3}

3 x + 5 \geq - \frac{7}{3} and 3 x + 5 \leq \frac{7}{3}

x \geq - \frac{22}{9} and x \leq - \frac{8}{9}

Merge Overlapping Intervals

- \frac{22}{9} \leq x \leq - \frac{8}{9}

5 - \frac{1}{2} x = \frac{5}{8} x + 2

9.6 = 1.2 b

9 x^{2} = 17

2 π + \frac{2 π}{3}

- 1.8 (6)^{2} + 14.4 (6)