Question

How do you solve the equation `abs(4-x)=7`?

Answer 1

`x=-3 and x=11`

Explanation:

The two vertical lines used this way are a special sort of brackets and they signify an 'Absolute' value. That is; whatever is between those lines is always considered as positive

So if the answer is positive 7 then what is inside those special brackets can only end up as two values. These are `+-7` in that:

`|+-7|=+7`

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Consider the case `4-x=-7`

Multiply both sides by (-1) `->` changes `-x` to `+x`

`-4+x=+7`

Add 4 to both sides `->` get rid of the -4 on the left

`-4+4+x=4+7`

`0+x=+11`

So one value is `x=11`
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Consider the case `4-x=+7`

Multiply by (-1)

`-4+x=-7`

So the other value is `x=-3`