What is |(7-3x)/2 |<= 1 ?

The solution to |(7-3x)/2 |<= 1 is 5/3 <= x<= 3

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|(7-3x)/2 |<= 1

\frac{7 - 3 x}{2} \leq 1

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

Interval Notation

[\frac{5}{3}, 3]

Decimal Notation

1.66666 \dots \leq x \leq 3

Solution steps

\frac{7 - 3 x}{2} \leq 1

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 1 \leq \frac{7 - 3 x}{2} \leq 1

\frac{7 - 3 x}{2} \geq - 1 and \frac{7 - 3 x}{2} \leq 1

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

Merge Overlapping Intervals

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

2 x^{2} - x - 28

14 g h - 18 h

(1 \frac{1}{2})^{2}

4 a^{2} b^{4}

x^{2} - 8 x - 24 = 0