How do you solve the compound inequality $3 t - 7 \geq 5$ $3t-7>=5$ and $2 t + 6 \leq 12$ $2t+6<=12$ ?

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Answer 1 · 2017-05-29T04:31:27

There are no values of $t$ $t$ that satisfy both inequalities.

We're looking for values of $t$ $t$ that satisfy both expressions. So let's solve both and see what we get:

$3 t - 7 \geq 5$ $3t-7ge5$

$3 t - 7 + 7 \geq 5 + 7$ $3t-7color(red)(+7)ge5color(red)(+7)$

$3 t \geq 12$ $3tge12$

$\frac{3 t}{3} \geq \frac{12}{3}$ $(3t)/color(red)(3)ge12/color(red)(3)$

$t \geq 4$ $color(blue)(tge4$

$2 t + 6 \leq 12$ $2t+6le12$

$2 t + 6 - 6 \leq 12 - 6$ $2t+6color(red)(-6)le12color(red)(-6)$

$2 t \leq 6$ $2tle6$

$\frac{2 t}{2} \leq \frac{6}{2}$ $(2t)/color(red)2le6/color(red)2$

$t \leq 3$ $color(blue)(tle3$

Are there any values of $t$ $t$ that satisfy both inequalities? No, and so therefore there are no solutions to this system of inequalities.

How do you solve the compound inequality 3t−7≥53t-7>=5 and 2t+6≤122t+6<=12?