please help :(
can someone please solve and graph |2x-5|+3 less than or equal to 10

Question

please help :(
can someone please solve and graph |2x-5|+3 less than or equal to 10

geerky42 · Answer

You need to  solve it by graphing?

anonymous · Answer

Nopee i need to solve then graph

geerky42 · Answer

Okay, 

Best thing to do first is to isolate absolute value, right?
Just subtract both sides by 3, then you should have $|2x-5|\le7$.

Any idea on how to get rid of absolute value?

anonymous · Answer

i think i add and subtract 5?

geerky42 · Answer

Well, that won't help get rid of it, though.

$$|2x-5|+5\le12$$

anonymous · Answer

i thought i leave the equation as it is after subtracting 3. and then solve it but also do another equation with 2x+5

geerky42 · Answer

Yeah kind of.

Let just say $2x+5 =a$

So here you have $|a|\le7$.

Do you know what value $a$ only can be?

anonymous · Answer

7

anonymous · Answer

?

geerky42 · Answer

Well, yeah $7\le7$

But there are more, right?

what about 6? 5? and so on?

geerky42 · Answer

Until 0?

geerky42 · Answer

Can we go behind 0 to negative number?

geerky42 · Answer

How far can we go?

anonymous · Answer

oh ok well i really just need help on this specific problem being that i have many more to do due by 10

geerky42 · Answer

Well, I'm just trying to help you understand how to solve it, so you don't have to ask similar questions again and again.

anonymous · Answer

of course thanks

geerky42 · Answer

But if you need answer for grade sake, well, sorry to say but we aren't allowed to do that lol...

geerky42 · Answer

Can you spare time?

anonymous · Answer

that isnt what i was asking for

geerky42 · Answer

Okay, back to stuffs.

$|a|\le7$

What range of number can $a$ be?

geerky42 · Answer

It only can goes from 7 to -7, right?

geerky42 · Answer

Because $|-7.1|\le7$ isn't correct, right?

geerky42 · Answer

So you can "translate"  $|a|\le 7$  to  $-7\le a\le7$

Makes sense so far?

anonymous · Answer

mhmm

geerky42 · Answer

So here $|2x-5|\le 7\quad\Longrightarrow\quad -7\le2x-5\le 7$

geerky42 · Answer

Now you can do algebra from here

anonymous · Answer

idk how to graph x$$x \le6,1$$

geerky42 · Answer

How did you get to $x\le6,1$?

anonymous · Answer

i solved it dude

anonymous · Answer

im sorry i dont have time for a lesson at the moment so im trying to rush and use prior knowledge

geerky42 · Answer

It's $-1\le x\le 6$

This mean x can only be in between -1 to 6 inclusive.

So you can graph like this:|dw:1430703011919:dw|