00:01
All right, so let's look at part a.
00:04
So we have the absolute value of x plus 4 is equal to 6.
00:11
So here we want to say, well, what can be inside that absolute value that will give us 6? well, we can have either 6 or negative 6.
00:21
So x plus 4 can equal 6 or x plus 4 can equal negative 6.
00:29
So let's solve the left equation first.
00:31
We subtract 4 from both sides.
00:35
And we get x equals 2 will satisfy this.
00:38
So we plug in 2, 2 plus 4 is 6.
00:41
Absolute value of 6 equals 6.
00:43
So we know this works.
00:45
Now let's solve the right equation.
00:48
Subtract 4 from both sides.
00:50
We get x equals negative 10.
00:52
Let's see if this works.
00:54
We plug in negative 10.
00:55
We get negative 10 plus 4 equals negative 6.
00:58
The absolute value of negative 6 is 6.
01:00
So this satisfies.
01:01
How we're going to write this is you're going to choose answer choice a and then it's going to look like the set of negative 10 comma 2 so that is for part a so part b is very similar except for now instead of an equal sign we have a greater than sign so let's see how this is going to change our answer so now we have x plus 4 is greater than six.
01:42
Also, we can have what's inside here has to be less than negative six.
01:55
So what we can think of this as is we're multiplying both sides by a negative.
02:02
And when we multiply by a negative, we have to flip the sign.
02:07
So that's why in this case, we have a flip here.
02:14
So let's look at the left equation.
02:16
So we have minus four, both sides.
02:20
So we have x has to be greater than two.
02:24
We can plug in a value say three, three plus four equals seven, absolute value of seven is greater than six.
02:31
So we know that satisfies.
02:33
So let's look at our right equation.
02:37
We have x is less than negative 10 because we subtract four from both sides.
02:47
So let's see if this works.
02:48
So if we have negative 11, negative 11 plus 4 is equal to negative 7.
02:58
Absolute value of negative 7 is greater than 6 because this is equal to 7...