What is |(6-5x)/(3+x)|<= 1/2 ?

The solution to |(6-5x)/(3+x)|<= 1/2 is 9/11 <= x<= 5/3

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|(6-5x)/(3+x)|<= 1/2

\frac{6 - 5 x}{3 + x} \leq \frac{1}{2}

\frac{9}{11} \leq x \leq \frac{5}{3}

Interval Notation

[\frac{9}{11}, \frac{5}{3}]

Decimal Notation

0.81818 \dots \leq x \leq 1.66666 \dots

Solution steps

\frac{6 - 5 x}{3 + x} \leq \frac{1}{2}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{2} \leq \frac{6 - 5 x}{3 + x} \leq \frac{1}{2}

\frac{6 - 5 x}{3 + x} \geq - \frac{1}{2} and \frac{6 - 5 x}{3 + x} \leq \frac{1}{2}

- 3 < x \leq \frac{5}{3} and (x < - 3 or x \geq \frac{9}{11})

Merge Overlapping Intervals

\frac{9}{11} \leq x \leq \frac{5}{3}

12 - x^{2} + x = 0

- 5 \cdot 6

\frac{3}{4} + \frac{2}{3}

(\frac{1}{2})^{\frac{1}{3}}

\frac{a ^{3}}{a ^{18}} \cdot a^{8}

What is |(6-5x)/(3+x)|<= 1/2 ?
The solution to |(6-5x)/(3+x)|<= 1/2 is 9/11 <= x<= 5/3