Question 1210247
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The equation {{{abs(x-5)=3}}} means x-5 is equal to either 3 or -3.  Solve the two equations separately.<br>
x-5 = 3
x = 3+5 = 8<br>
or<br>
x-5 = -3
x = -3+5 = 2<br>
ANSWERS: x = 8 or x = 2<br>
That's the formal algebraic way to solve the problem.<br>
There is another way to solve an absolute value equation like this that is usually easier (for me, at least) than the formal algebraic method.<br>
The equation {{{abs(x-a)=b}}} can be interpreted as meaning "the difference between x and a is equal to b".<br>
In this example, we have {{{abs(x-5)=3}}}, which we can interpret as saying "the difference between x and 5 is 3".<br>
Then look on a number line to find all the numbers (there will be two of them) that are 3 away from 5.<br>
3 to the right of 5 is 8; 3 to the left of 5 is 2.  So (again, of course!) the solutions are x = 8 and x = 2.<br>