What is | 4/7+2x|<= 2/5 ?

The solution to | 4/7+2x|<= 2/5 is -17/35 <= x<=-3/35

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| 4/7+2x|<= 2/5

\frac{4}{7} + 2 x \leq \frac{2}{5}

- \frac{17}{35} \leq x \leq - \frac{3}{35}

Interval Notation

[- \frac{17}{35}, - \frac{3}{35}]

Decimal Notation

- 0.48571 \dots \leq x \leq - 0.08571 \dots

Solution steps

\frac{4}{7} + 2 x \leq \frac{2}{5}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{2}{5} \leq \frac{4}{7} + 2 x \leq \frac{2}{5}

\frac{4}{7} + 2 x \geq - \frac{2}{5} and \frac{4}{7} + 2 x \leq \frac{2}{5}

x \geq - \frac{17}{35} and x \leq - \frac{3}{35}

Merge Overlapping Intervals

- \frac{17}{35} \leq x \leq - \frac{3}{35}

\frac{- 4}{9}

84 \geq - 7 (v - 9)

40 - 18 x - 40 x^{2}

2 x^{6} + 14 x^{4} + 4 x^{3}

\frac{2 π}{1.8}