SOLUTION: Solve the inequality. Give the solution set in interval notation. |5x-3|+5 > or equal to 9 The solution set is?

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Question 901994: Solve the inequality. Give the solution set in interval notation.
|5x-3|+5 > or equal to 9
The solution set is?

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
I am giving guidance but not a solution.

First, isolate the absolute value expression and treat it as a variable to solve.

Next, examine two cases for the input of the absolute value FUNCTION, as the entire expression INSIDE the absolute value function.

Either 5x-3 is POSITIVE OR ZERO; meaning that abs%285x-3%29=5x-3;
OR
5x-3 is NEGATIVE; meaning abs%285x-3%29=-%285x-3%29=-5x%2B3.

You can understand that second case if you would carefully examine according to the definition of absolute value and make reference to a number line.

Solve for both cases individually.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the inequality. Give the solution set in interval notation.
|5x-3|+5 > or equal to 9
The solution set is?

abs%285x+-+3%29+%2B+5+%3E=+9
abs%285x+-+3%29+%3E=+4 ------ Subtracting 5
5x+-+3+%3E=+4 OR 5x+-+3+%3C=+-+4
Solve for x in both cases.
Then do a check!!
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