What is -1/4 |3-2x|+3>= 1 ?

The solution to -1/4 |3-2x|+3>= 1 is -5/2 <= x<= 11/2

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-1/4 |3-2x|+3>= 1

- \frac{1}{4} ∣ 3 - 2 x ∣ + 3 \geq 1

- \frac{5}{2} \leq x \leq \frac{11}{2}

Interval Notation

[- \frac{5}{2}, \frac{11}{2}]

Decimal Notation

- 2.5 \leq x \leq 5.5

Solution steps

- \frac{1}{4} ∣ 3 - 2 x ∣ + 3 \geq 1

Move

3

to the right side

- \frac{1}{4} ∣ 3 - 2 x ∣ \geq - 2

Multiply both sides by

- 1

\frac{1}{4} ∣ 3 - 2 x ∣ \leq 2

Multiply both sides by

4

∣ 3 - 2 x ∣ \leq 8

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 8 \leq 3 - 2 x \leq 8

3 - 2 x \geq - 8 and 3 - 2 x \leq 8

x \leq \frac{11}{2} and x \geq - \frac{5}{2}

Merge Overlapping Intervals

- \frac{5}{2} \leq x \leq \frac{11}{2}

8^{\frac{3}{2}} \cdot \frac{2}{3}

∣ x + 5 ∣ \geq 9

(x - 3 - i) (x - 3 + i)

(x + 7) (x + 3) (x - 3) \geq 0

2 c^{2} + 11 c + 5

What is -1/4 |3-2x|+3>= 1 ?
The solution to -1/4 |3-2x|+3>= 1 is -5/2 <= x<= 11/2