What is |(2-3x)/7 |<= 2 ?

The solution to |(2-3x)/7 |<= 2 is -4<= x<= 16/3

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|(2-3x)/7 |<= 2

\frac{2 - 3 x}{7} \leq 2

- 4 \leq x \leq \frac{16}{3}

Interval Notation

[- 4, \frac{16}{3}]

Decimal Notation

- 4 \leq x \leq 5.33333 \dots

Solution steps

\frac{2 - 3 x}{7} \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq \frac{2 - 3 x}{7} \leq 2

\frac{2 - 3 x}{7} \geq - 2 and \frac{2 - 3 x}{7} \leq 2

x \leq \frac{16}{3} and x \geq - 4

Merge Overlapping Intervals

- 4 \leq x \leq \frac{16}{3}

\frac{3}{2} x - 5 > 4

- 5 w^{2} + 13 w - 6

- 4 b - 5 > - 25

- 5 = \frac{1}{3} (- 4) + b

ln (\frac{1}{4})