What is |3x+5|<= 7/2 ?

The solution to |3x+5|<= 7/2 is -17/6 <= x<=-1/2

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|3x+5|<= 7/2

∣ 3 x + 5 ∣ \leq \frac{7}{2}

- \frac{17}{6} \leq x \leq - \frac{1}{2}

Interval Notation

[- \frac{17}{6}, - \frac{1}{2}]

Decimal Notation

- 2.83333 \dots \leq x \leq - 0.5

Solution steps

∣ 3 x + 5 ∣ \leq \frac{7}{2}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{7}{2} \leq 3 x + 5 \leq \frac{7}{2}

3 x + 5 \geq - \frac{7}{2} and 3 x + 5 \leq \frac{7}{2}

x \geq - \frac{17}{6} and x \leq - \frac{1}{2}

Merge Overlapping Intervals

- \frac{17}{6} \leq x \leq - \frac{1}{2}

\frac{1}{∣ x - 2 ∣} > 2

\frac{3 x}{x ^{2} - 4} \leq 1

∣ 2 x - 5 ∣ \geq ∣ x + 2 ∣

∣ x ∣ \leq ∣ x + 1 ∣

\frac{( x ^{2} - ∣ x ∣ - 5 )}{( ∣ x ∣ - 7 )} \geq 2 x