Inequalities can be combined to be more efficient
By treating the combined inequality as two separate inequalities, you can easily solve
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.

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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?

$$4 < x \le 6$$

$$x > 4$$

$$x \ge 4$$

$$x > 6$$

Correct answer: $$x \ge 6$$

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: $$-1 \le x \le 3$$

$$-1 \le x \le 6$$

$$1 \le x \le 3$$

$$1 \le x \le 6$$