SOLUTION: 4|2x+3|-7<9

Question 1203651: 4|2x+3|-7<9

Found 3 solutions by ikleyn, MathLover1, greenestamps:
Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
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4|2x+3|-7 < 9
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They want you solve this inequality. Move -7 to the right with changing the sign. You will get 4*|2x+3| < 9 + 7, or 4*|2x+3| < 16. Divide both sides by 4. You will get |2x+3| <4. It means that -4 < 2x+3 < 4. Move 3 from the central part to the left and to the right, changing the sign. You will get -4 - 3 < 2x < 4 - 3, or -7 < 2x < 1. Divide everything by 2. You will get -3.5 < x < 0.5. It is your ANSWER: the solution set is -3.5 < x < 0.5, or the interval (-3.5,0.5), which does not include the endpoints.

Solved, with complete explanations.

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To see many other similar and different SOLVED problems on absolute value inequalities, look into the lesson
    - Solving absolute value inequalities
in this site.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

solution :

Interval notation:
(, )

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The solutions shown by the other tutors are good formal mathematical solutions.

A different method for solving absolute value problems like this is to interpret

as

"x is less than b units from a"

Applying that method to this problem....

This says that x is less than 2 units from -1.5.

2 units to the left of -1.5 is -3.5; 2 units to the right of -1.5 is 0.5. So the solution is

-3.5 < x < 0.5

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