What is -2|x+5|>=-6 ?

The solution to -2|x+5|>=-6 is -8<= x<=-2

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-2|x+5|>=-6

- 2 ∣ x + 5 ∣ \geq - 6

- 8 \leq x \leq - 2

Interval Notation

[- 8, - 2]

Solution steps

- 2 ∣ x + 5 ∣ \geq - 6

Multiply both sides by

- 1

2 ∣ x + 5 ∣ \leq 6

Divide both sides by

2

∣ x + 5 ∣ \leq 3

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3 \leq x + 5 \leq 3

x + 5 \geq - 3 and x + 5 \leq 3

x \geq - 8 and x \leq - 2

Merge Overlapping Intervals

- 8 \leq x \leq - 2

(2 x - 1)^{2} - (3 x + 6)^{2}

x (x - 1) = 0

\frac{1}{2} x \geq 0

19 - (2 x + 3) = 2 (x + 3) + x

a^{m + 4} \cdot b^{2 n + 3} - 3 a^{m + 1} \cdot b^{n + 2}