What is 9/2 (2+x)<= 1/3 (5x+14)<= 11-(3x)/2 ?

The solution to 9/2 (2+x)<= 1/3 (5x+14)<= 11-(3x)/2 is x<=-26/17

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9/2 (2+x)<= 1/3 (5x+14)<= 11-(3x)/2

\frac{9}{2} (2 + x) \leq \frac{1}{3} (5 x + 14) \leq 11 - \frac{3 x}{2}

x \leq - \frac{26}{17}

Interval Notation

(- \infty, - \frac{26}{17}]

Decimal Notation

x \leq - 1.52941 \dots

Solution steps

\frac{9}{2} (2 + x) \leq \frac{1}{3} (5 x + 14) \leq 11 - \frac{3 x}{2}

a \leq u \leq b

then

a \leq u and u \leq b

\frac{9}{2} (2 + x) \leq \frac{1}{3} (5 x + 14) and \frac{1}{3} (5 x + 14) \leq 11 - \frac{3 x}{2}

\frac{9}{2} (2 + x) \leq \frac{1}{3} (5 x + 14) : x \leq - \frac{26}{17}

\frac{1}{3} (5 x + 14) \leq 11 - \frac{3 x}{2} : x \leq 2

Combine the intervals

x \leq - \frac{26}{17} and x \leq 2

Merge Overlapping Intervals

x \leq - \frac{26}{17}

- 3 r^{2} - 2 r - 5 = 0

6 x y^{0}

4 x^{2} + 3 x y - 10 y^{2}

- 7 + 2 x \leq 5

\frac{15 x ^{2} - 23 x - 28}{5 x ^{2} - 6 x - 8} < 0

What is 9/2 (2+x)<= 1/3 (5x+14)<= 11-(3x)/2 ?
The solution to 9/2 (2+x)<= 1/3 (5x+14)<= 11-(3x)/2 is x<=-26/17