SOLUTION: Solve the inequality │2x - 3│≥ 1

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Question 1206735: Solve the inequality │2x - 3│≥ 1
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!




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solutions:



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Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The response from the other tutor shows a perfectly good standard formal algebraic solution.

A very different method for solving the problem is often much easier than the standard algebraic method.

The expression can be interpreted as saying the difference between x and a is equal to b. For example, means the difference between x and 5 is 3; that means x is either 5+3=8 or 5-3=2.

We can solve this problem using that method.



Divide everything by 2, because we need "x" to be by itself:



This absolute value inequality says that the difference between x and 1.5 is greater than or equal to 0.5.

1.5-0.5=1, so the difference between x and 1.5 is greater than or equal to 0.5 if x is less than or equal to 1;
1.5+0.5=2, so the difference between x and 1.5 is greater than or equal to 0.5 if x is greater than or equal to 2

So the inequality is satisfied if x is either less than or equal to 1, or greater than or equal to 2.

ANSWER: or


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