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Lesson 5 of 14
  • Year 11
  • Higher

Solving more complicated linear inequalities

I can solve more complicated linear inequalities.

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View unit
Lesson 5 of 14
New
New
  • Year 11
  • Higher

Solving more complicated linear inequalities

I can solve more complicated linear inequalities.

Download all

Lesson details

Key learning points

  1. Inequalities can be combined to be more efficient
  2. By treating the combined inequality as two separate inequalities, you can easily solve
  3. There may be a set of possible values, inequality notation can be used to communicate them efficiently

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 more complicated linear inequalities, download all teaching resources for free and adapt to suit your pupils' needs...

Pupils may need to review their understanding of solving equations before completing this lesson. The previous lesson is a good starting point for dealing with multiplying by -1 if pupils need a quick recap.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz

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6 Questions

Q1.
Which of these shows the solutions to the inequality $$3<2x+1$$?

$$x<1$$
Correct answer: $$x>1$$
$$x<2$$
$$x>2$$

Q2.
The solution to $$\frac{x+5}{3} \ge 3$$ is when $$x \ge $$

Correct Answer: 4

Q3.
Which of these values satisfy the inequality $$3 < x \le 4 $$ ?

$$x=2.5$$
$$x=3$$
Correct answer: $$x=3.5$$
Correct answer: $$x=4$$
$$x=4.5$$

Q4.
Which of these values satisfy the inequality $$-3 < x < -2 $$ ?

$$x=-3$$
$$x=-2$$
$$x=-3.5$$
Correct answer: $$x=-2.5$$
$$x=-1.5$$

Q5.
If $$-x > 3$$ which of the following is an equivalent inequality?

$$x<3$$
Correct answer: $$x<-3$$
$$x>3$$
$$x>-3$$

Q6.
Which inequality represents all values which satisfy both of the drawn inequalities?

An image in a quiz
$$4 < x \le 6$$
$$x > 4$$
$$x \ge 4$$
$$x > 6$$
Correct answer: $$x \ge 6$$

Assessment exit quiz

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6 Questions

Q1.
Which of these shows all solutions to the inequality $$19<2x+3 \le 21$$ ?

$$7 < x \le 9$$
Correct answer: $$8 < x \le 9$$
$$8 < x \le 12$$
$$9 < x \le 11$$
$$11 < x \le 12$$

Q2.
Which of these shows all solutions to the inequality $$-2 < -x < 1$$ ?

$$-2 < x < -1$$
$$-2 < x < 1$$
Correct answer: $$-1 < x < 2$$
$$1 < x < 2$$

Q3.
Which of these represents all values which satisfy both $$x>3$$ and $$4<x$$ ?

$$x>3$$
$$x<4$$
Correct answer: $$x>4$$
$$3<x<4$$
$$x<3$$ or $$x>4$$

Q4.
What are the solutions to the inequality $$x+1<3x+1<x+7$$ ?

$$-3 < x < 0$$
Correct answer: $$0< x < 3$$
$$1 < x < 3$$
$$1 < x < 6$$

Q5.
Which is the correct way to separate $$3x+2 \le 4x+3 \le 2x+9$$ into two inequalities to solve?

$$3x + 2 \le 4x$$ and $$3 \le 2x + 9$$
Correct answer: $$3x + 2 \le 4x + 3$$ and $$4x + 3 \le 2x + 9$$
$$4x+1 \ge 3x+2$$ and $$4x+3 \ge 2x+9$$
$$3x+2 \le 4x+3$$ and $$3x+2 \le 2x+9$$

Q6.
Solve the inequality $$3x+2 \le 4x+3 \le 2x+9$$.

Correct answer: $$-1 \le x \le 3$$
$$-1 \le x \le 6$$
$$1 \le x \le 3$$
$$1 \le x \le 6$$