SOLUTION: Thank you in advance for helping me with writing this problem in interval notation. The absolute value of 5x-3=10

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Question 149693This question is from textbook
: Thank you in advance for helping me with writing this problem in interval notation. The absolute value of 5x-3=10 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%285x-3%29=10 Start with the given equation


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

5x-3=-10 or 5x-3=10 Set the expression 5x-3 equal to the original value 10 and it's opposite -10




Now lets focus on the first equation 5x-3=-10


5x=-10%2B3Add 3 to both sides


5x=-7 Combine like terms on the right side


x=%28-7%29%2F%285%29 Divide both sides by 5 to isolate x



x=-7%2F5 Reduce






Now lets focus on the second equation 5x-3=10



5x=10%2B3Add 3 to both sides


5x=13 Combine like terms on the right side


x=%2813%29%2F%285%29 Divide both sides by 5 to isolate x



x=13%2F5 Reduce





So the solutions to abs%285x-3%29=10 are:

x=-7%2F5 and x=13%2F5