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Year 11
Foundation

Solving simple linear inequalities

I can solve simple linear inequalities.

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New
New
Year 11
Foundation

Solving simple linear inequalities

I can solve simple linear inequalities.

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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.


To help you plan your year 11 maths lesson on: Solving simple linear inequalities, download all teaching resources for free and adapt to suit your pupils' needs...

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.
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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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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: $$x={11\over 2}$$

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: $$x>-1$$
$$x<-1$$
$$x>1$$
$$x<1$$