What is | 2/5 x+1/2 |<= 1/10 ?

The solution to | 2/5 x+1/2 |<= 1/10 is -3/2 <= x<=-1

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| 2/5 x+1/2 |<= 1/10

\frac{2}{5} x + \frac{1}{2} \leq \frac{1}{10}

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

Interval Notation

[- \frac{3}{2}, - 1]

Decimal Notation

- 1.5 \leq x \leq - 1

Solution steps

\frac{2}{5} x + \frac{1}{2} \leq \frac{1}{10}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{10} \leq \frac{2}{5} x + \frac{1}{2} \leq \frac{1}{10}

\frac{2}{5} x + \frac{1}{2} \geq - \frac{1}{10} and \frac{2}{5} x + \frac{1}{2} \leq \frac{1}{10}

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

Merge Overlapping Intervals

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

2 (x - 5)^{2} = 20

∣ x + 5 ∣ > 7

7 + 5 x = 47

\frac{3 x y ^{2}}{6 x ^{4} y ^{7}}

3 \cdot 24

What is | 2/5 x+1/2 |<= 1/10 ?
The solution to | 2/5 x+1/2 |<= 1/10 is -3/2 <= x<=-1