SOLUTION: Solve. 2|3(x - 5)| + 3 = 9 There are two possible answers, and I'm unsure of what I'm doing wrong, i got -4,-7. Can you please work out this problem for me so i can see where i

Algebra ->  Inequalities -> SOLUTION: Solve. 2|3(x - 5)| + 3 = 9 There are two possible answers, and I'm unsure of what I'm doing wrong, i got -4,-7. Can you please work out this problem for me so i can see where i      Log On


   

Question 770911: Solve. 2|3(x - 5)| + 3 = 9
There are two possible answers, and I'm unsure of what I'm doing wrong, i got -4,-7. Can you please work out this problem for me so i can see where i made the mistake. Thank you :)
Found 2 solutions by algebrahouse.com, josgarithmetic:
Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
2|3(x - 5)| + 3 = 9
2|3x - 15| = 6 {used distributive property and subtracted 3 from each side}
|3x - 15| = 3 {divided each side by 2}
3x - 15 = 3 or 3x - 15 = -3 {absolute value is distance away from zero, therefore (3x - 15) could be 3 or -3}
3x = 18 or 3x = 12 {added 15 in each equation}
x = 6 or 4 {divided each side by 3}

For more help from me, visit: www.algebrahouse.com

Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
First, isolate the absolute value function.
abs%28x-5%29=%289-3%29%2F6
abs%28x-5%29=1
The factor of 3 inside the absolute value function is positive; so inside or outside the absolute value, not important.

Now treat for conditions of x-5%3C0 and x-5%3E=0
'
x-5%3C0 means abs%28x-5%29=-x-5=1
x%2B5=1
x=-4
'
x-5%3E=0 means abs%28x-5%29=x-5=1
x=1%2B5
x=6

RESULT: highlight%28x=-4%29 OR highlight%28x=6%29