**Writing and solving two step inequalities worksheet : **

Worksheet on writing and solving two step inequalities is much useful to the students who would like to practice solving word problems on inequalities.

1. Sum of two times of a number and 5 is less than -11. Find the number.

2. 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 ?

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 ?

**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

x ≥ 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

x ≥ 106

Hence, each member must raise at least $106 on average to meet the goal

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