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Does it Fit the Inequality? (2)

In this worksheet, students select solutions that fit the given algebraic inequality.

'Does it Fit the Inequality? (2)' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Look at the word INEQUALITY.  It is a bit like the word UNequal.

An inequality is like an equation but instead of both sides being equal they are unequal.

If two things are unequal, then one will be less than the other and one will be more than the other.

 

You should know the following symbols:

<     means less than

>     means more than

≤     means less than or equal to

≥     means more than or equal to

 

Example

If p + 3 ≤ 8, which of the following are possible solutions?

 

p = 3

p = 8

p = 10

p = -7.5

 

Working and answer

p + 3 ≤ 8

Subtract 3 from both sides

p ≤ 5

p can be any number less than or including 5.

So the possible answers are p = 3, p = -7.5

Select all the possible solutions to the inequality:

p + 4 ≤ 10

p = 6

p = 7

p = -7

p = 0

p = 9

Select all the possible solutions to the inequality:

p + 2 ≤ 5

p = 9

p = 0

p = -7

p = 7

p = 6

Select all the possible solutions to the inequality:

p - 1 ≤ -4

p = 9

p = 0

p = -7

p = 7

p = 6

Select all the possible solutions to the inequality:

p - 3 ≥ -6

p = 9

p = 0

p = -7

p = 7

p = 6

Select all the possible solutions to the inequality:

p + 2 ≥ -4

p = -7

p = 7

p = -6

p = 0

p = -9

Select all the possible solutions to the inequality:

q - 3 > 4

p = 9

q = 0

q = 9

q = 7

q = 12

Select all the possible solutions to the inequality:

q - 8 < -1

q = 6.9

q = 7

q = 12

q = 0

p = -9

Select all the possible solutions to the inequality:

m + 2 < -5.5

m = -9

m = 0

m = -6.9

m = 7

m = -12

Select all the possible solutions to the inequality:

m - 1 ≥ -8.5

m = -6.9

m = 7.5

m = -12

m = 0

m = -9

Select all the possible solutions to the inequality:

m - 2 ≤ 3.7

m = 0

m = -6.9

m = 7.5

m = -12

m = -9.7

  • Question 1

Select all the possible solutions to the inequality:

p + 4 ≤ 10

CORRECT ANSWER
p = 6
p = -7
p = 0
EDDIE SAYS
p + 4 ≤ 10 Subtract 4 from both sides p ≤ 6 All answers that are less than or equal to six will satisfy this inequality.
  • Question 2

Select all the possible solutions to the inequality:

p + 2 ≤ 5

CORRECT ANSWER
p = 0
p = -7
EDDIE SAYS
p + 2 ≤ 5 Subtract 2 from both sides p ≤ 3 All answers that are less than or equal to three will satisfy this inequality.
  • Question 3

Select all the possible solutions to the inequality:

p - 1 ≤ -4

CORRECT ANSWER
p = -7
EDDIE SAYS
p - 1 ≤ -4 Add 1 to both sides p ≤ -3 All answers that are less than or equal to minus 3 will satisfy this inequality.
  • Question 4

Select all the possible solutions to the inequality:

p - 3 ≥ -6

CORRECT ANSWER
p = 9
p = 0
p = 7
p = 6
EDDIE SAYS
p - 3 ≥ -6 Add 3 to both sides p ≥ -3 All answers that are greater than or equal to minus 3 will satisfy this inequality.
  • Question 5

Select all the possible solutions to the inequality:

p + 2 ≥ -4

CORRECT ANSWER
p = 7
p = -6
p = 0
EDDIE SAYS
p + 2 ≥ -4 Subtract 2 from both sides p ≥ -6 All answers that are greater than or equal to minus six will satisfy this inequality.
  • Question 6

Select all the possible solutions to the inequality:

q - 3 > 4

CORRECT ANSWER
q = 9
q = 12
EDDIE SAYS
q - 3 > 4 Add 3 to both sides q > 7 All answers that are greater than but not equal to seven will satisfy this inequality.
  • Question 7

Select all the possible solutions to the inequality:

q - 8 < -1

CORRECT ANSWER
q = 6.9
q = 0
EDDIE SAYS
q - 8 < -1 Add 8 to both sides q < 7 All answers that are less than but not equal to seven will satisfy this inequality.
  • Question 8

Select all the possible solutions to the inequality:

m + 2 < -5.5

CORRECT ANSWER
m = -9
m = -12
EDDIE SAYS
m + 2 < -5.5 Subtract 2 from both sides m < -7.5 All answers that are less than but not equal to minus seven and a half will satisfy this inequality.
  • Question 9

Select all the possible solutions to the inequality:

m - 1 ≥ -8.5

CORRECT ANSWER
m = -6.9
m = 7.5
m = 0
EDDIE SAYS
m - 1 ≥ -8.5 Add 1 to both sides m ≥ -7.5 All answers that are greater than but not equal to minus seven and a half will satisfy this inequality.
  • Question 10

Select all the possible solutions to the inequality:

m - 2 ≤ 3.7

CORRECT ANSWER
m = 0
m = -6.9
m = -12
m = -9.7
EDDIE SAYS
m - 2 ≤ 3.7 Add 2 to both sides m ≤ 5.7 All answers that are less than or equal to 5.7 will satisfy this inequality.
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