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

The solution to |2x-3|<= 2/5 is 13/10 <= x<= 17/10

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|2x-3|<= 2/5

∣ 2 x - 3 ∣ \leq \frac{2}{5}

\frac{13}{10} \leq x \leq \frac{17}{10}

Interval Notation

[\frac{13}{10}, \frac{17}{10}]

Decimal Notation

1.3 \leq x \leq 1.7

Solution steps

∣ 2 x - 3 ∣ \leq \frac{2}{5}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

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

x \geq \frac{13}{10} and x \leq \frac{17}{10}

Merge Overlapping Intervals

\frac{13}{10} \leq x \leq \frac{17}{10}

3 x - 1 = - 2 x + 4

\frac{0}{3}

(x + 4)^{2} + (x - 3)^{2} = (x + 5)^{2}

x^{2} - 3 x - 28 = 0

10 ∣ 3 x - 2 ∣ > 10