QuestionSolve the inequality and describe the graph of the solution.
Studdy Solution
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 means that the distance of from zero on the number line is greater than.
3. We need to find the values of that satisfy this condition.
STEP 2
We can solve the inequality by considering the two cases that make up the absolute value is greater than2, and is less than -2.
So, we have two inequalities to solve1.
2.
STEP 3
Let's solve the first inequality .
To isolate , we subtract3 from both sides of the inequality.
STEP 4
implify the inequality to find the solution for .
STEP 5
Now, let's solve the second inequality .
Again, to isolate , we subtract3 from both sides of the inequality.
STEP 6
implify the inequality to find the solution for .
STEP 7
So, the solutions to the inequality are and .This means that is either greater than -1 or less than -5.
STEP 8
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 , we shade the region to the right of -1.For , we shade the region to the left of -5.The shaded regions represent the solutions to the inequality.
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