What is (3x)/(5+2)<x+4<= x/(2+5) ?

The solution to (3x)/(5+2)<x+4<= x/(2+5) is -7<x<=-14/3

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(3x)/(5+2)<x+4<= x/(2+5)

\frac{3 x}{5 + 2} < x + 4 \leq \frac{x}{2 + 5}

- 7 < x \leq - \frac{14}{3}

Interval Notation

(- 7, - \frac{14}{3}]

Decimal Notation

- 7 < x \leq - 4.66666 \dots

Solution steps

\frac{3 x}{5 + 2} < x + 4 \leq \frac{x}{2 + 5}

a < u \leq b

then

a < u and u \leq b

\frac{3 x}{5 + 2} < x + 4 and x + 4 \leq \frac{x}{2 + 5}

\frac{3 x}{5 + 2} < x + 4 : x > - 7

x + 4 \leq \frac{x}{2 + 5} : x \leq - \frac{14}{3}

Combine the intervals

x > - 7 and x \leq - \frac{14}{3}

Merge Overlapping Intervals

- 7 < x \leq - \frac{14}{3}

0.37 < x < 0.99

\frac{1}{2} \leq 5 - \frac{x}{2} \leq 7

1 < \frac{( 3 x - 1 )}{( 2 x + 1 )} < 2

(5 x - 1) < (x + 1)^{2} < (7 x - 3)

- 0.1 \leq 3.4 x - 1.8 < 6.7

What is (3x)/(5+2)<x+4<= x/(2+5) ?
The solution to (3x)/(5+2)<x+4<= x/(2+5) is -7<x<=-14/3