SOLUTION: can you please help me solve these?? thanks! 1) abs(x/5)=2 2) 14+2 abs(3x+5)=26

Algebra ->  Absolute-value -> SOLUTION: can you please help me solve these?? thanks! 1) abs(x/5)=2 2) 14+2 abs(3x+5)=26      Log On


   



Question 322122: can you please help me solve these?? thanks!
1) abs(x/5)=2
2) 14+2 abs(3x+5)=26

Found 2 solutions by Jk22, jessica43:
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
1) abs(x/5)=2 => x/5=+-2 =>x=+-10
2) 14+2 abs(3x+5)=26 => 3x+5=+-6 => x=1/3, -11/3

Answer by jessica43(140) About Me  (Show Source):
You can put this solution on YOUR website!
The first thing you need to know is how to re-write absolute value problems. For example, abs(x)=3 means x=3 or x=-3.
For problem 1, abs(x/5)=2 can be re-written as -(x/5)=2 or (x/5)=2. Your next step is then to solve each equation for x.
-(x/5)=2
-(x/5)*(-5)=2*(-5) (Multiply each side by -5 to get ride of the denominator and make x positive)
x=-10
Then solve the other equation
(x/5)=2
(x/5)*(5)=2*(5)
x=10
Therefore the answer to 1 is x=-10 and x=10
2) You will follow the same rule for absolute values on this problem, but first we want to re-write the problem so we have the absolute value on its own side. This should always be your first step of absolute value problems.
14+2abs(3x+5)=26
14+2abs(3x+5)-14=26-14 (Subtract 14 from both sides)
2abs(3x+5)=12
(2abs(3x+5))/2=12/2 (Divide both sides by 2)
abs(3x+5)=6
Now you can re-write the absolute values as done in part 1.
abs(3x+5)= 6 can be re-written as -(3x+5)=6 or (3x+5)=6
Now solve each equation for x:
-(3x+5)=6
-3x-5=6 (then add 5 to each side)
-3x=11 (then divide each side by -3)
x=-11/3
Then solve the other equation
(3x+5)=6 (subtract 5 from each side)
3x=1 (divide each side by 3)
x=1/3
The answer for 2 is x=1/3 and x=-11/3
Hope that helps!