Math

QuestionSolve the inequality 3k+4>193k + 4 > 19 and express the solution set in interval and graph forms.

Studdy Solution

STEP 1

Assumptions1. The inequality to solve is 3k+4>193k +4 >19 . We are looking for all values of kk that satisfy this inequality3. The solution set should be given in interval notation

STEP 2

First, we need to isolate kk on one side of the inequality. We can do this by subtracting4 from both sides of the inequality.
k+44>194k +4 -4 >19 -4

STEP 3

implify the inequality.
3k>153k >15

STEP 4

Next, we need to further isolate kk by dividing both sides of the inequality by3.
3k3>153\frac{3k}{3} > \frac{15}{3}

STEP 5

implify the inequality to find the solution set.
k>5k >5

STEP 6

Now that we have the solution set, we can write it in interval notation. The inequality k>5k >5 corresponds to the interval (5,)(5, \infty).

STEP 7

For the graph, draw a number line and mark the point5. Since kk is greater than5, shade the region to the right of5. The point5 is not included in the solution set, so we use an open circle to indicate this.
The solution set is (5,)(5, \infty).

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