Question 1206735
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The response from the other tutor shows a perfectly good standard formal algebraic solution.<br>
A very different method for solving the problem is often much easier than the standard algebraic method.<br>
The expression {{{abs(x-a)=b}}} can be interpreted as saying the difference between x and a is equal to b.  For example, {{{abs(x-5)=3}}} means the difference between x and 5 is 3; that means x is either 5+3=8 or 5-3=2.<br>
We can solve this problem using that method.<br>
{{{abs(2x-3)>=1}}}<br>
Divide everything by 2, because we need "x" to be by itself:<br>
{{{abs(x-1.5)>=0.5}}}<br>
This absolute value inequality says that the difference between x and 1.5 is greater than or equal to 0.5.<br>
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<br>
So the inequality is satisfied if x is either less than or equal to 1, or greater than or equal to 2.<br>
ANSWER: {{{x<=1}}} or {{{x>=2}}}<br>