Question

How do you solve `11= | d - 5| + 4`?

Answer 1

Answer is `d=-2` and `d=12`

Explanation:

This is an absolute valued equation. So it must have two solution. Since it is a piece meal function.

Since the graph has sharp bend at `d=5` we get two intervals to solve That is `(-oo,5]` and `[5,oo)` .So let's solve in first interval.

In that interval the
domain(without absolute value) make a negative range . So a negative times negative is positive.

So `11=-(d-5)+4`
`or,11=-d+9`
`:.d=-2`

Note we are only multiplying `(d-5)` since it gets negative first and 4 is just a constant.
And our solution is in the domain we are concerned.

Let's solve in second interval. `[5,oo)` Here all domain produce positive domain.
So `11=(d-5)+4`
`or, 11=-1+d`
`:.d=12`
Note: This is just a linear equation . So it had only two intervals. While you are solving absolute value problems of higher polynomials. You have to test whether your solution is in the domain or not. If not in the domain. Then discard it. It is an "false" solution. Try solving a quadratic absolute value equation. It might be trickier.