What is 4|2w+3|-7<= 9 ?

The solution to 4|2w+3|-7<= 9 is -7/2 <= w<= 1/2

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4|2w+3|-7<= 9

4 ∣ 2 w + 3 ∣ - 7 \leq 9

- \frac{7}{2} \leq w \leq \frac{1}{2}

Solution steps

4 ∣ 2 w + 3 ∣ - 7 \leq 9

Move

7

to the right side

4 ∣ 2 w + 3 ∣ \leq 16

Divide both sides by

4

∣ 2 w + 3 ∣ \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq 2 w + 3 \leq 4

2 w + 3 \geq - 4 and 2 w + 3 \leq 4

w \geq - \frac{7}{2} and w \leq \frac{1}{2}

Merge Overlapping Intervals

- \frac{7}{2} \leq w \leq \frac{1}{2}

\frac{a}{5} - 18 = 2

\frac{p}{2} - 2 \leq 1

8 x^{2} - 22 x - 21

(x^{4})^{\frac{1}{2}}

2 x^{2} - 9 x + 9 = 0