What is 8-|2x-1|>= 6 ?

The solution to 8-|2x-1|>= 6 is -1/2 <= x<= 3/2

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8-|2x-1|>= 6

8 - ∣ 2 x - 1 ∣ \geq 6

- \frac{1}{2} \leq x \leq \frac{3}{2}

Interval Notation

[- \frac{1}{2}, \frac{3}{2}]

Decimal Notation

- 0.5 \leq x \leq 1.5

Solution steps

8 - ∣ 2 x - 1 ∣ \geq 6

Move

8

to the right side

- ∣ 2 x - 1 ∣ \geq - 2

Multiply both sides by

- 1

∣ 2 x - 1 ∣ \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq 2 x - 1 \leq 2

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

x \geq - \frac{1}{2} and x \leq \frac{3}{2}

Merge Overlapping Intervals

- \frac{1}{2} \leq x \leq \frac{3}{2}

\frac{π}{2} - π

\frac{2}{5} - \frac{1}{6}

m^{2} - 9 m + 8

(\frac{2}{5})^{4}

\frac{9}{16} - 1