What is (7x+2)/(4-2x)>= 0 ?

The solution to (7x+2)/(4-2x)>= 0 is -2/7 <= x<2

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(7x+2)/(4-2x)>= 0

\frac{7 x + 2}{4 - 2 x} \geq 0

- \frac{2}{7} \leq x < 2

Interval Notation

[- \frac{2}{7}, 2)

Decimal Notation

- 0.28571 \dots \leq x < 2

Solution steps

\frac{7 x + 2}{4 - 2 x} \geq 0

Factor

\frac{7 x + 2}{4 - 2 x} : \frac{7 x + 2}{- 2 ( x - 2 )}

\frac{7 x + 2}{- 2 ( x - 2 )} \geq 0

Simplify

\frac{7 x + 2}{- 2 ( x - 2 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( 7 x + 2 ) ( - 1 )}{- 2 ( x - 2 )} \leq 0 \cdot (- 1)

Simplify

\frac{7 x + 2}{2 ( x - 2 )} \leq 0

Multiply both sides by

2

\frac{2 ( 7 x + 2 )}{2 ( x - 2 )} \leq 0 \cdot 2

Simplify

\frac{7 x + 2}{x - 2} \leq 0

Identify the intervals

- \frac{2}{7} \leq x < 2

\frac{5}{15}

- 0.5 (x - 4) = 1.5

- 6 m^{2} = - 414

\frac{5}{6} + \frac{1}{6}

0.1 \cdot 0.10005