# How do you solve and graph abs(5t-2)<=6?

Apr 20, 2018

Absolute values measure distance, so that $| - x |$ equals $x$. But when you try to solve for this, you have to consider that the question could be $| x |$ or $| - x |$ and you will get the same answer. So you need to solve for both situations

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$5 t - 2 \le 6$

solve for $t$

$5 t \le 8$

$t < = \frac{8}{5}$

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$- \left(5 t - 2\right) \le 6$

$5 t - 2 \ge - 6$

note that the direction of the sign changed

$5 t \ge - 4$

$t \ge - \frac{4}{5}$

So, we are saying that $t$ is greater than $- \frac{4}{5}$ but less than $\frac{8}{5}$, which you can see in this graph