document.write( "Question 1210247: |x − 5| = 3 \n" ); document.write( "

Algebra.Com's Answer #851740 by greenestamps(13289) $\"\"$ $\"About$

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\n" ); document.write( "The equation $\"abs%28x-5%29=3\"$ means x-5 is equal to either 3 or -3. Solve the two equations separately.

\n" ); document.write( "x-5 = 3
\n" ); document.write( "x = 3+5 = 8

\n" ); document.write( "or

\n" ); document.write( "x-5 = -3
\n" ); document.write( "x = -3+5 = 2

\n" ); document.write( "ANSWERS: x = 8 or x = 2

\n" ); document.write( "That's the formal algebraic way to solve the problem.

\n" ); document.write( "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.

\n" ); document.write( "The equation $\"abs%28x-a%29=b\"$ can be interpreted as meaning \"the difference between x and a is equal to b\".

\n" ); document.write( "In this example, we have $\"abs%28x-5%29=3\"$ , which we can interpret as saying \"the difference between x and 5 is 3\".

\n" ); document.write( "Then look on a number line to find all the numbers (there will be two of them) that are 3 away from 5.

\n" ); document.write( "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.

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