What is 9-|3x-2|>= 1 ?

The solution to 9-|3x-2|>= 1 is -2<= x<= 10/3

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9-|3x-2|>= 1

9 - ∣ 3 x - 2 ∣ \geq 1

- 2 \leq x \leq \frac{10}{3}

Interval Notation

[- 2, \frac{10}{3}]

Decimal Notation

- 2 \leq x \leq 3.33333 \dots

Solution steps

9 - ∣ 3 x - 2 ∣ \geq 1

Move

9

to the right side

- ∣ 3 x - 2 ∣ \geq - 8

Multiply both sides by

- 1

∣ 3 x - 2 ∣ \leq 8

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 8 \leq 3 x - 2 \leq 8

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

x \geq - 2 and x \leq \frac{10}{3}

Merge Overlapping Intervals

- 2 \leq x \leq \frac{10}{3}

r^{3} - 8

5 z^{2} + 40 z + 80

c^{2} - 9 c + 20

8 (x + 1) = 6 - 2 (8 x + 7)

\frac{9}{9}