Solve the problem. See ExamplesFor what values of x would the triangle have a perimeter of...

Solve the problem. See Examples

For what values of x would the triangle have a perimeter of at least 72?

EXAMPLE Using a Linear Inequality to Solve a Rental Problem

A rental company charges $15 to rent a chain saw, plus $2 per hr. Tom Ruhberg can spend no more than $35 to clear some logs from his yard. What is the maximum amount of time he can use the rented saw?

Step 1 Read the problem again.

Step 2 Assign a variable. Let x = the number of hours he can rent the saw.

Step 3 Write an inequality. He must pay $15, plus $2x, to rent the saw for x hours, and this amount must be no more than $35.

Step 4 Solve.

Step 5 State the answer. He can use the saw for a maximum of 10 hr. (Of course, he may use it for less time, as indicated by the inequality x ≤ 10.)

Step 6 Check. If Tom uses the saw for 10 hr, he will spend 15 + 2(10) = 35 dollars, the maximum amount.

EXAMPLE Finding an Average Test Score

John Baker has grades of 86, 88, and 78 on his first three tests in geometry. If he wants an average of at least 80 after his fourth test, what are the possible scores he can make on that test?

Step 1 Read the problem again.

Step 2 Assign a variable. Let x = John’s score on his fourth test.

Step 3 Write an inequality.

Step 4 Solve.

Step 5 State the answer. He must score 68 or more on the fourth test to have an average of at least 80.

Step 6 Check.

(Also show that a score greater than 68 gives an average greater than 80.)