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

The solution to 8-|2x-3|>= 2 is -3/2 <= x<= 9/2

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8-|2x-3|>= 2

8 - ∣ 2 x - 3 ∣ \geq 2

- \frac{3}{2} \leq x \leq \frac{9}{2}

Interval Notation

[- \frac{3}{2}, \frac{9}{2}]

Decimal Notation

- 1.5 \leq x \leq 4.5

Solution steps

8 - ∣ 2 x - 3 ∣ \geq 2

Move

8

to the right side

- ∣ 2 x - 3 ∣ \geq - 6

Multiply both sides by

- 1

∣ 2 x - 3 ∣ \leq 6

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 6 \leq 2 x - 3 \leq 6

2 x - 3 \geq - 6 and 2 x - 3 \leq 6

x \geq - \frac{3}{2} and x \leq \frac{9}{2}

Merge Overlapping Intervals

- \frac{3}{2} \leq x \leq \frac{9}{2}

20 x^{3} y^{7} + 28 x^{4} y^{3} + 32 x^{4} y^{2}

8 - 9

(\frac{1}{a})^{3}

∣ 3 - 8 ∣

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