# Inequalities Worksheet

Inequalities Worksheet
• Page 1
1.
Write the inequality, $\frac{z}{5}$> 30, as a word sentence.
 a. Carol has z candies. She divided equally among 5 children. Each child got 30 candies. b. Carol has z candies. She divided them equally among 5 children. Each child got less than 30 candies. c. Mary has z candies. She divided them equally among 6 children. Each child got less than 30 candies. d. Mary has z candies. She divided them equally among 5 children. Each child got more than 30 candies.

#### Solution:

'Mary has z candies. She divided them equally among 6 children. Each child got less than 30 candies', is represented by ' z / 6< 30 '.

'Carol has z candies. She divided equally among 5 children. Each child got 30 candies', is represented by ' z / 5= 30 '.

'Carol has z candies. She divided them equally among 5 children. Each child got less than 30 candies', is represented by ' z / 5< 30 '.

'Mary has z candies. She divided them equally among 5 children. Each child got more than 30 candies', is represented by ' z / 5> 30 '.

The inequality ' z / 5> 30 ' represents to the situation 'Mary has z candies. She divided them equally among 5 children. Each child got more than 30 candies'.

2.
Write the inequality, y × 5 < 30, as a word sentence.
 a. Maria bought y ribbons for $5 each. She paid more than$30. b. Maria bought y ribbons for $6 each. She paid more than$30. c. Maria bought y ribbons for $6 each. She paid less than$30. d. Maria bought y ribbons for $5 each. She paid less than$30.

#### Solution:

'Maria bought y ribbons for $5 each. She paid more than$30', is represented by 'y × 5 > 30'.

'Maria bought y ribbons for $6 each. She paid less than$30', is represented by 'Y × 6 < 30'.

'Maria bought y ribbons for $6 each. She paid more than$30', is represented by 'Y × 6 > 30'.

'Maria bought y ribbons for $5 each. She paid less than$30', is represented by 'Y × 5 < 30'.

The inequality 'y × 5 < 30' is represented by the situation 'Maria bought y ribbons for $5 each. She paid less than$30'.

3.
Which of the following best describes the inequality, 9x < 200?
 a. Cost of x items at $9 each is less than$200. b. Cost of x items at $9 each is decreased by$200. c. Cost of x items at $9 each is more than$200. d. Cost of x items at $9 each is increased by$200.

#### Solution:

'Cost of x items at $9 each is decreased by$200', is represented by '9x - 200'.

'Cost of x items at $9 each is more than$200', is represented by '9x > 200'

'Cost of x items at $9 each is increased by$200', is represented by '9x + 200'.

'Cost of x items at $9 each is less than$200', is represented by '9x < 200'.

The inequality '9x < 200' is represented by the situation 'Cost of x items at $9 each is less than$200'.

4.
Write the inequality, x - 5 > 30, as a word sentence.
 a. Clara had x flowers. She got 5 more from Rosy. Number of flowers she had is less than 30. b. Clara had x flowers. She gave 5 to Rosy. Number of flowers she had is more than 30. c. Clara had x flowers. She got 5 more from Rosy. Number of flowers she had is more than 30. d. Clara had x flowers. She gave 5 to Rosy. Number of flowers she had is less than 30.

#### Solution:

'Clara had x flowers. She got 5 more from Rosy. Number of flowers she had is more than 30', is represented by ' x + 5 > 30'.

'Clara had x flowers. She gave 5 to Rosy. Number of flowers she had is less than 30', is represented by ' x - 5 < 30'.

'Clara had x flowers. She got 5 more from Rosy. Number of flowers she had is less than 30', is represented by ' x + 5 < 30'.

'Clara had x flowers. She gave 5 to Rosy. Number of flowers she had is more than 30', is represented by ' x - 5 > 30'

The inequality 'x - 5 > 30' is represented by the situation, 'Clara had x flowers. She gave 5 to Rosy. Number of flowers she had is more than 30'.

5.
Identify a graph that shows $x$ ≤ 5.

 a. Graph 4 b. Graph 3 c. Graph 2 d. Graph 1

6.
Which of the graphs represents the inequality, $a$ + 3 > 2?

 a. Graph 1 b. Graph 3 c. Graph 4 d. Graph 2

7.
Which inequality is represented by the graph?

 a. 5$x$ < 10 b. 4$x$ < - 2 c. 9 > 3$y$ d. 2$x$ > 4

8.
Which of the graphs represents the inequality, $b$ > - 5?

 a. Graph 4 b. Graph 3 c. Graph 1 d. Graph 2

9.
Identify a graph that represents the inequality, $h$ - 7 ≤ - 5.

 a. Graph 2 b. Graph 4 c. Graph 3 d. Graph 1

10.
Write an inequality for the graph.

 a. $x$ > 0 b. $x$ ≤ 0 c. $x$ < 0 d. $x$ ≥ 0

#### Solution:

A solution of an inequality is any value of the variable that makes the inequality true.

An open circle means 0 is not a solution of the inequality.

So, the inequality represented by the graph is x < 0.