What is -(1/3)|6-5x|+2>= 1 ?

The solution to -(1/3)|6-5x|+2>= 1 is 3/5 <= x<= 9/5

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-(1/3)|6-5x|+2>= 1

- (\frac{1}{3}) ∣ 6 - 5 x ∣ + 2 \geq 1

\frac{3}{5} \leq x \leq \frac{9}{5}

Solution steps

- \frac{1}{3} ∣ 6 - 5 x ∣ + 2 \geq 1

Move

2

to the right side

- \frac{1}{3} ∣ 6 - 5 x ∣ \geq - 1

Multiply both sides by

- 1

\frac{1}{3} ∣ 6 - 5 x ∣ \leq 1

Multiply both sides by

3

∣ 6 - 5 x ∣ \leq 3

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3 \leq 6 - 5 x \leq 3

6 - 5 x \geq - 3 and 6 - 5 x \leq 3

x \leq \frac{9}{5} and x \geq \frac{3}{5}

Merge Overlapping Intervals

\frac{3}{5} \leq x \leq \frac{9}{5}

∣ x ∣ + ∣ x - 1 ∣ < x + 4

3 x^{2} - 5 x > - 6

∣ 2 x + 1 ∣ > x

∣ x - 1 ∣ < 0

∣ 3 x - 2 ∣ \leq x + 1

What is -(1/3)|6-5x|+2>= 1 ?
The solution to -(1/3)|6-5x|+2>= 1 is 3/5 <= x<= 9/5