Question

How do you solve `|11x - 46| = - 42`?

Answer 1

`x=4/11, 11`

Explanation:

With absolute value questions like this, we need to remember that the absolute value will take what is inside the bracket and return a positive value. So for example, if I write:

`absx=3`

`x` could be 3. It could also be `-3`. So we need to solve for both positive and negative values within the absolute value brackets.

Positive

`abs(11x-46)=-42`

`11x-46=-42`

`11x=4`

`color(blue)(ul(bar(abs(color(black)(x=4/11))))`

Negative

`abs(11x-46)=-42`

`-(11x-46)=-42`

`-11x+46=-42`

`-11x=-88`

`color(blue)(ul(bar(abs(color(black)(x=11))))`

We can see this in a graph:

graph{(y-abs(11x-46))(y-0x-42)=0 [-8.17, 17.14, 38.35, 51.01]}