Question

How do you solve `- 2abs(x - 3) + 10 = - 4`?

Answer 1

`x=10" or "x=-4`

Explanation:

Isolate the `color(blue)"absolute value"`

subtract 10 from both sides.

`-2|x-3|cancel(+10)cancel(-10)=-4-10`

`rArr-2|x-3|=-14`

divide both sides by - 2

`cancel(-2)/cancel(-2)|x-3|=(-14)/(-2)`

`rArr|x-3|=7larrcolor(red)"absolute value isolated on left"`

Equations with an absolute value usually have 2 solutions.

We now solve `x-3=color(red)(+-)7`

`color(blue)"Solution 1"`

`x-3=color(red)(+)7rArrx=7+3=10`

`color(blue)"Solution 2"`

`x-3=color(red)(-)7rArrx=-7+3=-4`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`•x=10to-2|10-3|+10=-14+10=-4`

`•x=-4to-2|-4-3|+10=-14+10=-4`

`rArrx=10" or "x=-4" are the solutions"`