Math Snap

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line. It is always non-negative.
. The inequality $|x+3|>$ means that the distance of $x+3$ from zero on the number line is greater than.
3. We need to find the values of $x$ that satisfy this condition.

STEP 2

We can solve the inequality by considering the two cases that make up the absolute value $x+$ is greater than2, and $x+$ is less than -2.
So, we have two inequalities to solve1. $x+>2$
2. $x+<-2$

STEP 3

Let's solve the first inequality $x+3>2$.
To isolate $x$, we subtract3 from both sides of the inequality.
$$x+3-3>2-3$$

STEP 4

implify the inequality to find the solution for $x$.
$$x>2-3$$$$x>-1$$

STEP 5

Now, let's solve the second inequality $x+3<-2$.
Again, to isolate $x$, we subtract3 from both sides of the inequality.
$$x+3-3<-2-3$$

STEP 6

implify the inequality to find the solution for $x$.
$$x<-2-3$$$$x<-5$$

STEP 7

So, the solutions to the inequality $|x+3|>2$ are $x>-1$ and $x<-5$.This means that $x$ is either greater than -1 or less than -5.

To graph the solutions, we draw a number line and mark the points -1 and -5.We then shade the regions of the number line that correspond to the solutions.For $x>-1$, we shade the region to the right of -1.For $x<-5$, we shade the region to the left of -5.The shaded regions represent the solutions to the inequality.