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}

Interval Notation

[\frac{3}{5}, \frac{9}{5}]

Decimal Notation

0.6 \leq x \leq 1.8

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}

\frac{y + 3}{6} < 2

6 - 6 \frac{x}{5} < 18

- x^{2} + 4 x - 1 = 0

3 t^{2} - 12 t + 11 = 0

x^{2} - 3 x + x y - 3 y