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Solving more complicated linear inequalities

I can solve more complicated linear inequalities.

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Lesson 5 of 14

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Year 11

Solving more complicated linear inequalities

I can solve more complicated linear inequalities.

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Lesson details

Key learning points

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.

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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).

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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?

$$4 < x \le 6$$

$$x > 4$$

$$x \ge 4$$

$$x > 6$$

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

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

$$1 \le x \le 3$$

$$1 \le x \le 6$$

Lesson appears in

UnitMaths / Inequalities

Maths

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Solving more complicated linear inequalities

Solving more complicated linear inequalities

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

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

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

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

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

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

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

Assessment exit quiz

6 Questions

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

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

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

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

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

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

Lesson appears in

UnitMaths / Inequalities

Maths

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

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

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

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

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

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

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

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

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

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

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

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