New

Year 11

Foundation

Problem solving with linear inequalities

I can use my knowledge of inequalities to solve problems.

Download all resources

Share activities with pupils

New

Year 11

Foundation

Problem solving with linear inequalities

I can use my knowledge of inequalities to solve problems.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

View new resources

Slide deck

Download slide deck

Skip slide deck

Lesson details

Key learning points

When handling a project, there are often constraints
Constraints exist for a variety of reasons, such as cost or supply limitations
Finding a set of possible solutions allows you to work within the constraints

Keywords

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

Common misconception

We are only interested in points that are in the region satisfied by all inequalities.

With practical contexts, such as project management, it is useful to know when one constraint is not being met as it can suggest where additional resources (if available) should be allocated.

Consider having pupils investigate what additional capacity would mean by changing the constraints. What options are available if the constraints still existed but had less restrictive values?

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

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Starter quiz

Download starter quiz

6 Questions

Q1.

$$15x+25y=1500$$ is an equation whereas $$15x+25y<1500$$ is an .

Correct Answer: inequality

Q2.

Which of these is the point of intersection of these two linear equations?

$$(0, 0)$$

$$(0, 4)$$

$$(4, 0)$$

Correct answer: $$(4, 12)$$

$$(12, 4)$$

Q3.

For the equation $$c=10+6m$$ what is the value of $$c$$ when $$m=9$$? $$c=$$ .

Correct Answer: 64

Q4.

Solve $$5x<x+28$$.

$$x>7$$

Correct answer: $$x<7$$

$$x<28$$

$$x<5$$

$$x>5$$

Q5.

Which of these values satisfy this inequality? $${3x+6y}\le{450}$$

Correct answer: $$(60,30)$$

Correct answer: $$(30,60)$$

Correct answer: $$(70,20)$$

$$(20,70)$$

$$(60,50)$$

Q6.

A taxi firm charge a fixed rate of $$£4$$ per journey plus $$£1.50$$ per mile travelled. The cost of your journey cannot exceed $$£16$$. Which inequality models this scenario?

$$4m+1.5<16$$

$$4+1.5m<16m$$

$$4+1.5m<16$$

Correct answer: $${4+1.5m}\le16$$

$${4m+1.5}\le16$$

Exit quiz

Download exit quiz

6 Questions

Q1.

The graph shows the charges of three taxi firms. The coordinate pair $$(3,9)$$ is the point of __________ of the graphs of taxi firms 'a' and 'b'.

Correct answer: intersection

intercept

inequality

Q2.

In what region does taxi firm 'a' charge less than taxi firm 'b'?

Correct answer: $$m<3$$

$$m>3$$

$$m\le3$$

$$m<4$$

$$m>4$$

Q3.

In what region does taxi firm 'c' charge less than taxi firm 'a'?

$$m<4$$

Correct answer: $$m>4$$

$$m\geq4$$

$$m<8$$

$$m>8$$

Q4.

These inequalities model a company's packaging and production constraints. Which of these points satisfies the production constraint but not the packaging constraint?

$$(10, 80)$$

$$(60, 80)$$

Correct answer: $$(60, 10)$$

$$(10, 10)$$

Q5.

These inequalities model a company's packaging and production constraints. Which of these points satisfy both the production and the packaging constraints?

Correct answer: $$(50,15)$$

$$(15,50)$$

$$(40,30)$$

$$(30,40)$$

Correct answer: $$(60,0)$$

Q6.

These inequalities model a company's packaging and production constraints. Which coordinate pair is the point where both production and packaging are optimised?

Correct Answer: (50,20), (50, 20)