WRITING AND SOLVING TWO STEP INEQUALITIES 

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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