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

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 #2x=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 #2x=-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 #|2x-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