SOLUTION: How do I solve this absolute value equation:3/5+2|2-3/4x|=7. The answers are -8/5 or 104/15 but I do not know how the answers are found. Please reply ASAP. Thanks.

Algebra ->  Absolute-value -> SOLUTION: How do I solve this absolute value equation:3/5+2|2-3/4x|=7. The answers are -8/5 or 104/15 but I do not know how the answers are found. Please reply ASAP. Thanks.      Log On


   

Question 339198: How do I solve this absolute value equation:3/5+2|2-3/4x|=7. The answers are -8/5 or 104/15 but I do not know how the answers are found. Please reply ASAP. Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F5%2B2%2Aabs%282-%283%2F4%29x%29=7 Start with the given equation.


2%2Aabs%282-%283%2F4%29x%29=7-3%2F5 Subtract 3%2F5 from both sides.


2%2Aabs%282-%283%2F4%29x%29=32%2F5 Combine like terms.


abs%282-%283%2F4%29x%29=%2832%2F5%29%281%2F2%29 Multiply both sides by 1%2F2


abs%282-%283%2F4%29x%29=32%2F10 Multiply.


abs%282-%283%2F4%29x%29=16%2F5 Reduce.


Now remember that if abs%28x%29=a, then x=a or x=-a


This means that if abs%282-%283%2F4%29x%29=16%2F5, then 2-%283%2F4%29x=16%2F5 or 2-%283%2F4%29x=-16%2F5


Let's solve the first equation:


2-%283%2F4%29x=16%2F5 Start with the given equation.


20%282-%283%2Fcross%284%29%29x%29=20%2816%2Fcross%285%29%29 Multiply both sides by the LCD 20 to clear any fractions.


40-15x=64 Distribute and multiply.


-15x=64-40 Subtract 40 from both sides.


-15x=24 Combine like terms on the right side.


x=%2824%29%2F%28-15%29 Divide both sides by -15 to isolate x.


x=-8%2F5 Reduce.


So one solution is x=-8%2F5

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Now let's solve 2-%283%2F4%29x=-16%2F5


2-%283%2F4%29x=-16%2F5 Start with the given equation.


20%282-%283%2Fcross%284%29%29x%29=20%28-16%2Fcross%285%29%29 Multiply both sides by the LCD 20 to clear any fractions.


40-15x=-64 Distribute and multiply.


-15x=-64-40 Subtract 40 from both sides.


-15x=-104 Combine like terms on the right side.


x=%28-104%29%2F%28-15%29 Divide both sides by -15 to isolate x.


x=104%2F15 Reduce.


So another solution is x=104%2F15


This means that the solutions to 3%2F5%2B2%2Aabs%282-%283%2F4%29x%29=7 are x=-8%2F5 or x=104%2F15


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website.

Jim