# Equations with Absolute Value

by Amy McKain
(Brazil, IN)

Here is the question. It is 3 absolute value of x divided by 9 plus 7 equals 8.

### Comments for Equations with Absolute Value

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 Jan 25, 2011 Rating Equations with Absolute Value by: Karin You solve this equation very similar to a regular equation with the absolute value. We are going to address the absolute value in the last step. The problem: ((3|x|)/9) + 7 = 8 Step 1: Subtract 7 from both sides. ((3|x|)/9) +7-7 = 8 -7 ((3|x|)/9) = 1 Step 2: Get rid of the fraction by multiplying all terms by 9. 9((3|x|)/9)=1(9) 3|x| = 9 Step 3: Divide by 3 on both sides. (3|x|)/3 = 9/3 |x| = 3 Now we are left with the absolute value of x = 3. Remember that absolute value means that the value of the number inside of that absolute value sign is always positive. So we can say that: x = 3 or -x = 3 If -x =3 then we would multiply all terms by -1 to make x positive. -1(-x) = 3(-1) x = -3 Basically you know that 3 or -3 could be inside of the absolute value symbol and the value of that number will always be 3. Check your answer: 3|3|/9 + 7 = 8 9/9 + 7 = 8 1+7 = 8 So, we know that 3 works. Now check -3 3|-3|/9 + 7 = 8 3(3)/9 + 7 = 8 9/9 + 7 = 8 1+7 = 8 -3 also works. Therefore, x could be equal to 3 or -3. x = 3 x = -3 I hope this helps, Karin

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