What is 8-|2x-3|>= 4 ?

The solution to 8-|2x-3|>= 4 is -1/2 <= x<= 7/2

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8-|2x-3|>= 4

8 - ∣ 2 x - 3 ∣ \geq 4

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

Interval Notation

[- \frac{1}{2}, \frac{7}{2}]

Decimal Notation

- 0.5 \leq x \leq 3.5

Solution steps

8 - ∣ 2 x - 3 ∣ \geq 4

Move

8

to the right side

- ∣ 2 x - 3 ∣ \geq - 4

Multiply both sides by

- 1

∣ 2 x - 3 ∣ \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq 2 x - 3 \leq 4

2 x - 3 \geq - 4 and 2 x - 3 \leq 4

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

Merge Overlapping Intervals

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

\frac{x}{2} + 12 = 84

21 + 9 j - 10 = - 277

4 (x - 6) + 2 x - 4 \geq 3 (x - 7) + 10 x

3 y^{3} - 9 y^{2}

(2 x - 6) (3 x - 4) = 0