What is 8-|2x-5|>= 2 ?

The solution to 8-|2x-5|>= 2 is -1/2 <= x<= 11/2

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8-|2x-5|>= 2

8 - ∣ 2 x - 5 ∣ \geq 2

- \frac{1}{2} \leq x \leq \frac{11}{2}

Solution steps

8 - ∣ 2 x - 5 ∣ \geq 2

Move

8

to the right side

- ∣ 2 x - 5 ∣ \geq - 6

Multiply both sides by

- 1

∣ 2 x - 5 ∣ \leq 6

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 6 \leq 2 x - 5 \leq 6

2 x - 5 \geq - 6 and 2 x - 5 \leq 6

x \geq - \frac{1}{2} and x \leq \frac{11}{2}

Merge Overlapping Intervals

- \frac{1}{2} \leq x \leq \frac{11}{2}

\frac{5 - 6}{18}

- 5 p + 9 \leq 34

∣ x + 1 ∣ = 8

2 + 2 k \geq 10

2 x^{2} + 3 x + 3 = 0