What is 9-|2x-1|>= 5 ?

The solution to 9-|2x-1|>= 5 is -3/2 <= x<= 5/2

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9-|2x-1|>= 5

9 - ∣ 2 x - 1 ∣ \geq 5

- \frac{3}{2} \leq x \leq \frac{5}{2}

Interval Notation

[- \frac{3}{2}, \frac{5}{2}]

Decimal Notation

- 1.5 \leq x \leq 2.5

Solution steps

9 - ∣ 2 x - 1 ∣ \geq 5

Move

9

to the right side

- ∣ 2 x - 1 ∣ \geq - 4

Multiply both sides by

- 1

∣ 2 x - 1 ∣ \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq 2 x - 1 \leq 4

2 x - 1 \geq - 4 and 2 x - 1 \leq 4

x \geq - \frac{3}{2} and x \leq \frac{5}{2}

Merge Overlapping Intervals

- \frac{3}{2} \leq x \leq \frac{5}{2}

x^{4} - 9 x^{2} - 3 x^{3} + 27 x - 10 x^{2} + 90

3400

4 x \leq 16

\frac{g}{3} = \frac{3}{4}

125 a^{3} - 216 b^{3}