8- l x-4 l =5 How to figure out absolute value equations..?

[Ladybug]

I need help figuring out equations that have absolute values. I know the easy ones, like abs(2x-3) =9. The answer to that would be 6 and a negative 3 in place of the x. I need 2 answers for each equations, one that will give the same numbers, but one negative/one positive.

1) 8-lx-4l =5

2) 2 l2x-3l +1=11

3) 3 l2x-3l +12=3

4) -2 l3-2xl +9=1

I'm working on homework and out of 35 those were the ones I couldn't find an answer for. I would love a thorough explanation of how to solve these. Thanks so much!!

 

[skeeter]

in each equation, isolate the absolute value expression.

for example ...

2|2x-3| + 1 = 11

2|2x-3| = 10

|2x-3| = 5

can you solve it now?

 

[Ladybug]

That makes sense!

But on this one, 8-lx-4l =5...does it become -lx-4l = -3? How do I deal with that negative sign in front of lx-4l?

Thanks!

 

[skeeter]

multiply both sides by -1 ... you get |x-4| = 3

 

[Ladybug]

Oh, ok. Got that about multiplying by -1. Thanks!

I did have one more question...

in each equation, isolate the absolute value expression.

for example ...

2|2x-3| + 1 = 11

2|2x-3| = 10

|2x-3| = 5
can you solve it now?

How did 2|2x-3| = 10 become |2x-3| = 5? Shouldn't it become |2x-3| = 8, if we subtract the 2 in front of |2x-3| :?: Thanks again![/color][/size]

 

[jwpaine]

Oh, ok. Got that about multiplying by -1. Thanks!

I did have one more question...

in each equation, isolate the absolute value expression.

for example ...

2|2x-3| + 1 = 11

2|2x-3| = 10

|2x-3| = 5
can you solve it now?

How did 2|2x-3| = 10 become |2x-3| = 5? Shouldn't it become |2x-3| = 8, if we subtract the 2 in front of |2x-3| :?: Thanks again!

2 is multiplied by |2x-3| so you divide both sides by 2

2|2x-3| = 10
(2|2x-3|)/2 = 10/2
|2x-3| = 5

 

[skeeter]

if 2 times (something) = 10, then (something) = ?

 

[Ladybug]

How did 2|2x-3| = 10 become |2x-3| = 5? Shouldn't it become |2x-3| = 8, if we subtract the 2 in front of |2x-3| :?: Thanks again!

2 is multiplied by |2x-3| so you divide both sides by 2

2|2x-3| = 10
(2|2x-3|)/2 = 10/2
|2x-3| = 5

But how does 2 l2x-3l when divided by 2 remain the same, inside the absolute value bars? And how does the 2 disappear? Thanks for your help, once again!

 

[Deleted member 4993]

how does 2 l2x-3l when divided by 2 remain the same, inside the absolute value bars? And how does the 2 disappear?

How would you solve for 'a' if

2*a + 1 = 11

 

[marshall1432]

|2x-3|=5
Then you have to get the 2 variable equations from that

2x-3=5 OR 2x-3=-5
2x=8 OR 2x=-2
x=4 OR x=-1
Thats the answer

 

[Ladybug]

|2x-3|=5
Then you have to get the 2 variable equations from that

2x-3=5 OR 2x-3=-5
2x=8 OR 2x=-2
x=4 OR x=-1
Thats the answer

Thanks! I already got both those answers, so now I know they're right.