What is 6-|2x-3|>= 2 ?

The solution to 6-|2x-3|>= 2 is -1/2 <= x<= 7/2

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6-|2x-3|>= 2

6 - ∣ 2 x - 3 ∣ \geq 2

- \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

6 - ∣ 2 x - 3 ∣ \geq 2

Move

6

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}

- 2 \cdot 1

∣ 2 x - 4 ∣ = 10

(x + 4)^{2} - (8 x + 7)^{2}

(81 x^{12})^{1.25}

x - y - x y + x^{2}