How do you solve 3|5x-1|+9(less than or equal to) 23

Question

jdoe0001 · Answer

by $\bf \mathbb{NIKE}$  :P

jdoe0001 · Answer

you'd do it the same way you'd any equation more or less
so $\bf 3|5x-1|+9 \le 23$   you proceed about the same as you'd with $\bf 3|5x-1|+9 = 23$

jdoe0001 · Answer

just keep in mind that |5x-1| is really meant to be
+1(5x-1)    AND -1(5x-1)

so $\bf 3|5x-1|+9 \le 23\
\color{blue}{3\left[1(5x-1)\right]\le 23\
3\left[-1(5x-1)\right]\le 23}$

anonymous · Answer

I feel stupid...thank you

jdoe0001 · Answer

yw

jdoe0001 · Answer

the one exception you want to keep in mind is that, in inequalities
whenever you multiply or divide or exponentialize by a negative value
you $\bf \color{red}{\text{ flip the sign}}$
only when you use a negative factor though

jdoe0001 · Answer

so say   
-2x < 10 
# multiplying both sides by -2
x > -5

jdoe0001 · Answer

well, multiplying by - 1/2 rather