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Year 11
Higher

Solving simple linear inequalities

I can solve simple linear inequalities.

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New
New
Year 11
Higher

Solving simple linear inequalities

I can solve simple linear inequalities.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. A linear inequality is solved using the rules of algebraic manipulation
  2. Multiplying or dividing by a negative number reverses the inequality sign
  3. This is due to a reflection in the number line at 0
  4. This can also be shown algebraically

Keywords

  • Inequality - An inequality is used to show that one expression may not be equal to another.

Common misconception

Dividing or multiplying by -1 does not change the inequality sign.

2 < 3 becomes -2 > -3 when both sides are multiplied by -1.

Pupils may need to review their understanding of negative numbers before this lesson. Some pupils may struggle with the idea that -5 < -3 if their understanding of negative numbers is not secure.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of these inequalities are valid?
Correct answer: $$3<5$$
$$-3<-5$$
Correct answer: $$4>-2$$
$$-4>2$$
Q2.
Which of these values satisfy the inequality $$x \ge -3$$ ?
-4
Correct answer: -3
Correct answer: -2
-4.5
-3.5
Q3.
Which of these diagrams could represent the inequality $$a>3$$ ?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q4.
The solution to the equation $$3x-5=7$$ is when $$x=$$ .
Correct Answer: 4
Q5.
The solution to the equation $$3(x+4)=21$$ is when $$x=$$ .
Correct Answer: 3
Q6.
What is the solution to this equation $$\frac{4x+3}{5}=5$$ ?
$$x=-2$$
$$x=-{1\over2}$$
$$x={2\over 11}$$
$$x={1\over2}$$
Correct answer: $$x={11\over 2}$$

Exit quiz

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6 Questions

Q1.
The solution to the inequality $$3a-2 \ge 4$$ is when $$a \ge$$ .
Correct Answer: 2
Q2.
Which of these satisfies the inequality $$2b+3 < 5$$ ?
Correct answer: $$b=-1$$
Correct answer: $$b=0$$
Correct answer: $$b=0.5$$
$$b=1$$
$$b=2.5$$
Q3.
Which of these shows all solutions to the inequality $${a\over 3} + 4 \le 7$$ ?
$$a \le 1$$
$$a<1$$
Correct answer: $$a \le 9$$
$$a<9$$
$$a \ge 33$$
Q4.
Which of these represents all solutions to the inequality $$8<4(x-3)$$ ?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q5.
If $$-x<-4$$ which of the following is an equivalent inequality?
$$x<4$$
$$x<-4$$
Correct answer: $$x>4$$
$$x>-4$$
Q6.
Which of these shows all solutions to the inequality $$5-3x<8$$ ?
Correct answer: $$x>-1$$
$$x<-1$$
$$x>1$$
$$x<1$$