What is |-2/3 x+4|<= 5 ?

The solution to |-2/3 x+4|<= 5 is -3/2 <= x<= 27/2

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|-2/3 x+4|<= 5

- \frac{2}{3} x + 4 \leq 5

- \frac{3}{2} \leq x \leq \frac{27}{2}

Interval Notation

[- \frac{3}{2}, \frac{27}{2}]

Decimal Notation

- 1.5 \leq x \leq 13.5

Solution steps

- \frac{2}{3} x + 4 \leq 5

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 5 \leq - \frac{2}{3} x + 4 \leq 5

- \frac{2}{3} x + 4 \geq - 5 and - \frac{2}{3} x + 4 \leq 5

x \leq \frac{27}{2} and x \geq - \frac{3}{2}

Merge Overlapping Intervals

- \frac{3}{2} \leq x \leq \frac{27}{2}

- 14 + 2 r = 2

35 0^{2} + b^{2} = 610.2 1^{2}

3 (1) + y = 7

6 c^{2} + 12 c + 6

7 x^{3} - 28 x