Question

Which of the following values of x is in the solution set of 2|x + 4| > 14?

A. x = 0
B. x = 1
C.x = –3
D.x = –12

Answer 1

To answer this question, you could solve for the possible values of X in the equation or you could try each of the four answers given and see if they work. Let's solve for the possible values for X - I think it's more fun!

To solve for X in an equation with an absolute value is very similar to solving for X in a normal equation.
First, divide both sides by 2. Now you have | x + 4 | > 7
From here, we can address the absolute value sign by breaking this equation into 2 possibilities. The positive possibility: (X + 4) > 7 or the negative possibility: (X + 4) < -7

Let's try the positive possibility first: X + 4 > 7
Subtracting 4 from both sides gives you X > 7
Now let's look at the 4 multiple choice answers. None of the choices are greater than 7! We must have to solve the negative possibility to get the right answer.

Let's look at the negative possibility: X + 4 < -7
Subtracting 4 from both sides gives you X < -11
Does any choice work for this value of X? Yes! Try checking your answer by inserting that value for X back in the original equation and see if the inequality is true.