QuestionSolve for in the inequalities or and graph the solution.
Studdy Solution
STEP 1
Assumptions1. The given inequalities are and . We need to solve for in both inequalities3. We need to graph the solution
STEP 2
Let's start by solving the first inequality . We can do this by multiplying both sides of the inequality by4.
STEP 3
implify the left side of the inequality by cancelling out the's.
STEP 4
implify the right side of the inequality.
STEP 5
Now, to isolate , add2 to both sides of the inequality.
STEP 6
implify both sides of the inequality.
STEP 7
Now let's solve the second inequality . We can do this by multiplying both sides of the inequality by3.
STEP 8
implify the left side of the inequality by cancelling out the3's.
STEP 9
implify the right side of the inequality.
STEP 10
Now, to isolate , add to both sides of the inequality.
STEP 11
implify both sides of the inequality.
STEP 12
Now we have the solutions for the inequalities and .
STEP 13
To graph these solutions, we plot them on a number line. We plot and as the endpoints.
STEP 14
Since , we draw an open circle at and a line extending to the left, indicating all numbers less than .
STEP 15
Since , we draw a closed circle at and a line extending to the right, indicating all numbers greater than or equal to .
The solution to the inequalities is or .
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