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

##### 1 Answer

OR

#### Explanation:

First you can seperate the equation into two possible cases to get rid of the absolute value sign:

For case number one, you have to isolate the variable,

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

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,

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

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

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

So, the answers to

***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**