Example 1 :
Sum of two times of a number and 5 is less than -11. Find the number.
Solution :
Let x be the number.
Step 1 :
Write the inequality.
2x + 5 < -11
Step 2 :
Solve the inequality using Subtraction and Division properties of Inequality.
Subtract 5 on from both sides.
(2x + 5) - 5 < -11 - 5
2x < -16
Divide both sides by 2
(2x) / 2 < (-16) / 2
x < -8
So, the number is any value less than -8.
Example 2 :
A mountain climbing team is camped at an altitude of 18,460 feet on Mount Everest. The team wants to reach more than 29,029-foot summit within 6 days. Find the average number of feet per day the team must climb to accomplish its objective.
Solution :
Let x be the average number of feet per day the team must climb to accomplish its objective.
Step 1 :
Write the inequality.
6x + 18460 ≥ 29029
Step 2 :
Solve the inequality using Subtraction and Division properties of Inequality.
Subtract 18460 on from both sides.
(6x + 18460) - 18460 ≥ 29029 - 18460
6x ≥ 10569
Divide both sides by 6
(6x) / 6 ≥ (10569) / 6
x ≥ 1761.5
So, the team must climb at least 1761.5 feet per day to accomplish its objective.
Example 3 :
The 45 members of the glee club are trying to raise more than $6,000, so they can compete in the state championship. They already have $1,230. Find the amount that each member must raise, on average, to meet the goal?
Solution :
Let x be the amount that each member must raise on average to meet the goal.
Step 1 :
Write the inequality.
45x + 1230 ≥ 6000
Step 2 :
Solve the inequality using Subtraction and Division properties of Inequality.
Subtract 1230 on from both sides.
(45x + 1230) - 1230 ≥ 6000 - 1230
45x ≥ 4770
Divide both sides by 45
(45x) / 45 ≥ (4770) / 45
x ≥ 106
So, each member must raise at least $106 on average to meet the goal
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