What is | 1/2-((5x))/3 |<= 5 ?

The solution to | 1/2-((5x))/3 |<= 5 is -27/10 <= x<= 33/10

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| 1/2-((5x))/3 |<= 5

\frac{1}{2} - \frac{( 5 x )}{3} \leq 5

- \frac{27}{10} \leq x \leq \frac{33}{10}

Solution steps

\frac{1}{2} - \frac{5 x}{3} \leq 5

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 5 \leq \frac{1}{2} - \frac{5 x}{3} \leq 5

\frac{1}{2} - \frac{5 x}{3} \geq - 5 and \frac{1}{2} - \frac{5 x}{3} \leq 5

x \leq \frac{33}{10} and x \geq - \frac{27}{10}

Merge Overlapping Intervals

- \frac{27}{10} \leq x \leq \frac{33}{10}

\frac{( ∣ x + 2 ∣ + x )}{( x + 1 )} > 1

∣ x + 7 ∣ + ∣ x ∣ \leq \frac{1}{2}

x^{2} - 5 x + 6 < x^{2} - 2 x

x^{2} - 1 > 0

\frac{( ∣ x ∣ - 3 )}{( ∣ x ∣ - 5 )} < 0

What is | 1/2-((5x))/3 |<= 5 ?
The solution to | 1/2-((5x))/3 |<= 5 is -27/10 <= x<= 33/10