# WRITING AND SOLVING TWO STEP INEQUALITIES

Writing and Solving Two Step Inequalities :

In this section, we will learn how to create an inequality for the given word problem by using algebraic reasoning and solve for the unknown quantity.

## Writing and Solving Two Step Inequalities - Examples

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

Hence, 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

≥  1761.5

Hence, 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

≥ 106

Hence, each member must raise at least \$106 on average to meet the goal After having gone through the stuff given above, we hope that the students would have understood, how to write and solve two step inequalities.

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