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Popular >

5-2|3-2x|<= 1

Solution

5 - 2 ∣ 3 - 2 x ∣ \leq 1

Solution

x \leq \frac{1}{2} or x \geq \frac{5}{2}

+2

Interval Notation

(- \infty, \frac{1}{2}] \cup [\frac{5}{2}, \infty)

Decimal Notation

x \leq 0.5 or x \geq 2.5

Solution steps

5 - 2 ∣ 3 - 2 x ∣ \leq 1

Move

5

to the right side

- 2 ∣ 3 - 2 x ∣ \leq - 4

Multiply both sides by

- 1

2 ∣ 3 - 2 x ∣ \geq 4

Divide both sides by

2

∣ 3 - 2 x ∣ \geq 2

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

3 - 2 x \leq - 2 or 3 - 2 x \geq 2

3 - 2 x \leq - 2 or 3 - 2 x \geq 2

x \leq \frac{1}{2} or x \geq \frac{5}{2}

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n^{2} - 2 n - 48

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6 y^{4} - 15 y^{3}

Frequently Asked Questions (FAQ)

What is 5-2|3-2x|<= 1 ?
The solution to 5-2|3-2x|<= 1 is x<= 1/2 \lor x>= 5/2