What is | 3/2-(5x)/3 |<= 2 ?

The solution to | 3/2-(5x)/3 |<= 2 is -3/10 <= x<= 21/10

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| 3/2-(5x)/3 |<= 2

\frac{3}{2} - \frac{5 x}{3} \leq 2

- \frac{3}{10} \leq x \leq \frac{21}{10}

Interval Notation

[- \frac{3}{10}, \frac{21}{10}]

Decimal Notation

- 0.3 \leq x \leq 2.1

Solution steps

\frac{3}{2} - \frac{5 x}{3} \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq \frac{3}{2} - \frac{5 x}{3} \leq 2

\frac{3}{2} - \frac{5 x}{3} \geq - 2 and \frac{3}{2} - \frac{5 x}{3} \leq 2

x \leq \frac{21}{10} and x \geq - \frac{3}{10}

Merge Overlapping Intervals

- \frac{3}{10} \leq x \leq \frac{21}{10}

6 x - 9 \leq 2 x + 7

- 0.1 x^{2} + 10 = 0

4 x^{2} + 6 x - 9 = 0

\frac{3}{8} x = 21

x^{2} - 9 x = - 18

What is | 3/2-(5x)/3 |<= 2 ?
The solution to | 3/2-(5x)/3 |<= 2 is -3/10 <= x<= 21/10