What is 9-|2x-3|>= 5 ?

The solution to 9-|2x-3|>= 5 is -1/2 <= x<= 7/2

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9-|2x-3|>= 5

9 - ∣ 2 x - 3 ∣ \geq 5

- \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

9 - ∣ 2 x - 3 ∣ \geq 5

Move

9

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}

a + \frac{1}{2} a + \frac{2}{3} a

∣ 3 x - 2 ∣ > 7

2 (2 m) + 4 (4 m + 2) = 108

25 x^{2} - 20 x + 4 = 0

\frac{x}{\frac{y}{x}}