Question

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

Answer 1

`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 `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