How do you solve for x: |2x − 9| = 11?

Apr 4, 2018

$x = - 1$
OR
$x = 10$

Explanation:

First you can seperate the equation into two possible cases to get rid of the absolute value sign:
1)2x-9=11
2)2x-9=-11

For case number one, you have to isolate the variable, $x$.

TO do that you must get rid of the constant, -9, by adding the additive inverse*, or in our case, 9 on both sides to get $2 x = 20$.

Finally you can get rid of the coefficient, or the 2 in our case, by multiplying the multiplicative inverse**, in our case -2 on both sides to get our variable, $x = 10$

For case number two, you also need to isolate the variable, $x$.

You do the same exact thing as case number one, adding the additive inverse on both sides. In equation 2, the constant is still -9 so you have to add 9, the additive inverse, on both sides to get $2 x = - 2$

Finally, you can multiply the coefficient,2, by the multiplicative inverse, -2 to get the variable by itself.Once you do this you get $x = - 1$

So, the answers to $| 2 x - 9 | = 11$ are $x = 10$ and $x = - 1$

*an additive inverse is the number that, when added to a number $x$, yields zero

**a multiplicative inverse is the number that, when multiplied to a number $x$ yields 1