Which values of x will make the absolute value equation true? |x – 4| = 7 a. {–3, 3} b. {–3, 11} c. {–11, 11} d. no solution

Let's check each answer choice

Checking choice A
Plug in x = -3
|x-4| = 7
|-3-4| = 7 ... replace x with -3
|-7| = 7
7 = 7
We have a true equation so x = -3 works

Plug in x = 3
|x-4| = 7
|3-4| = 7 ... replace x with 3
|-1| = 7
1 = 7
The last equation is false so x = 3 is not a solution. We can cross choice A off the list.

Checking choice B
We already checked x = -3 (see above in choice A). All we need to do is check x = 11
|x-4| = 7
|11-4| = 7 replace x with 11
|7| = 7
7 = 7
We have a true equation so x = 11 works
Since x = -3 and x = 11 work, this means we have the proper solution set {-3, 11}. So this means choice B is the final answer

For the sake of completeness, let's check choice C. 
Plug in x = -11
|x-4| = 7
|-11-4| = 7 ... replace x with -11
|-15| = 7
15 = 7
The last equation is false so choice C can be ruled out as well.

We can cross choice D off the list since we found there is a solution set and it is {-3, 11} back in choice B.

Let's say that we didn't have these answer choices and it was a fill in the blank type of problem. Here's how to find the two solutions
|x-4|=7
x-4=7 or x-4=-7   break up the absolute value
x-4+4=7+4 or x-4+4=-7+4 add 4 to each side (for each equation)
x = 11 or x = -3
x = -3 or x = 11
So the solution set is {-3, 11}


Final Choice B) {-3, 11}

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