We're still going to use the fact that if the absolute value of A is equal to B.

Then either A is equal to B, or A is equal to -B but we're just going to have

to check our answers at the end. Okay, so applying this, we have that x +

4 then is either equal to 3x +8 or x + 4 = -(3x + 8), but be careful to use

parenthesis here. Again, we'll solve each equation

separately. Let's begin with the first equation.

We'll bring the 3x to the left and the 4 to the right.

Which gives us x - 3x = 8 - 4, or -2x = 4, and then dividing both sides by -2

gives us x = -2. And now, let's solve the second equation.

We'll begin by distributing the negative to both of these two terms.

That is we have x + 4 =- 3x - 8. And now we bring the -3x to the left and

the 4 to the right which gives x + 3x = -8 -4 or 4x = -12 and then dividing both

sides by 4, we get x = -3. Now remember, we must check these answers

by plugging each of them into the original equation wherever we see an x.

So, let's start with x = -2. The question is, is the absolute value of

-2 + 4 = 3(-2) + 8, or as the absolute value of 2 = -6 + 8 which is 2.

And yes, it is. So -2 works.

What about -3? The question is, is the absolute value of -3 + 4 = 3(-3) + 8.

Or, is the absolute value of -3 + 4 which is 1 = to -9 + 8, which is -1.

And no this is not true. Because the absolute value of 1 is equal

to 1, not -1. Which means we need to cross off -3.

Therefore, our only answer is x = -2. So let's write back here then, our answer

is x = -2. And this is how we solve absolute value

equations. Just be very careful to check your

answers when that right hand side is not a positive number.

Thank you, and we'll see you next time.

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