What is (7t+4)/(3t-8)>=-1 ?

The solution to (7t+4)/(3t-8)>=-1 is t 8/3

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(7t+4)/(3t-8)>=-1

\frac{7 t + 4}{3 t - 8} \geq - 1

t \leq \frac{2}{5} or t > \frac{8}{3}

Interval Notation

(- \infty, \frac{2}{5}] \cup (\frac{8}{3}, \infty)

Decimal Notation

t \leq 0.4 or t > 2.66666 \dots

Solution steps

\frac{7 t + 4}{3 t - 8} \geq - 1

Rewrite in standard form

\frac{10 t - 4}{3 t - 8} \geq 0

Factor

\frac{10 t - 4}{3 t - 8} : \frac{2 ( 5 t - 2 )}{3 t - 8}

\frac{2 ( 5 t - 2 )}{3 t - 8} \geq 0

Divide both sides by

2

\frac{\frac{2 ( 5 t - 2 )}{3 t - 8}}{2} \geq \frac{0}{2}

Simplify

\frac{5 t - 2}{3 t - 8} \geq 0

Identify the intervals

t \leq \frac{2}{5} or t > \frac{8}{3}

lo g_{625} (5)

\frac{18 !}{( 18 - 2 ) !}

\frac{( x - 4 ) ( x + 3 )}{( x - 5 ) ( x + 8 )} \geq 0

2 x^{2} = 7 x + 5

x^{2} + 1 = 3 x

What is (7t+4)/(3t-8)>=-1 ?
The solution to (7t+4)/(3t-8)>=-1 is t<= 2/5 \lor t> 8/3