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Year 11
Higher

Relating graphical solutions to algebraic solutions for inequalities

I can solve inequalities graphically and relate this to solving algebraically.

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New
New
Year 11
Higher

Relating graphical solutions to algebraic solutions for inequalities

I can solve inequalities graphically and relate this to solving algebraically.

Download all resources
Share activities with pupils

Link copied to clipboard

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

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Lesson details

Key learning points

  1. By comparing the graphs to the algebraic approach, you can compare the representations of the solution set
  2. The point of intersection is an important point

Keywords

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

  • Region - A region is an area that graphically represents the solutions to one or more inequalities. Every coordinate pair within the region satisfies the inequalities that define the region.

Common misconception

All inequalities are graphed with solid lines.

When graphed, strict inequalities are indicated with a dashed line. This is important as it visually tells us that values on the line will not satisfy the inequality.


To help you plan your year 11 maths lesson on: Relating graphical solutions to algebraic solutions for inequalities, download all teaching resources for free and adapt to suit your pupils' needs...

Encourage pupils to identify the region that satisfies multiple inequalities in different ways: graphically, testing a point, algebraically.
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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Starter quiz

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6 Questions

Q1.
$$(4,-2)$$ is the point of of these two linear graphs.
An image in a quiz
Correct Answer: intersection
Q2.
Solve $$5x-7\geq{2x+38}$$.
Correct answer: $$x\geq15$$
$$x>15$$
$$x\le15$$
$$x<15$$
$$x=15$$
Q3.
Which inequality is represented by this region?
An image in a quiz
Correct answer: $$x>-4$$
$$x<-4$$
$$x=-4$$
$$x\le-4$$
$$x\geq-4$$
Q4.
Solve $${x+8}<{2x+14}\le{6}$$.
$$-6<x$$
$$-6<x<-4$$
$$-6\le{x}<-4$$
Correct answer: $$-6<x\le-4$$
$$x\le-4$$
Q5.
Which inequality is represented by this region?
An image in a quiz
$$-2\le{y}\le4$$
$$-2<{y}<4$$
Correct answer: $$-2<{y}\le4$$
$$-2<{x}\le4$$
$$4<{y}\le-2$$
Q6.
Solve $${1-3x}>10$$.
Correct answer: $$x<-3$$
$$x>-3$$
$$x<3$$
$$x>3$$

Exit quiz

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6 Questions

Q1.
This graph shows us that the __________ $$2x+8>2-x$$ is $$x>-2$$.
An image in a quiz
Correct answer: solution to
intersection of
equation for
Q2.
This graph shows that the region $$x<4$$ is the solution to which inequality?
An image in a quiz
Correct answer: $$2x-3<x+1$$
$$2x-3>x+1$$
$$2x-3\le{x+1}$$
$$2x-3\geq{x+1}$$
Q3.
Use the graph to solve $$x+1<2x-3$$.
An image in a quiz
$$x<4$$
Correct answer: $$x>4$$
$$x<-1$$
$$x>-1$$
$$x>-2$$
Q4.
Use the graph to solve $$-4x-9<2x-3$$.
An image in a quiz
$$x<-2$$
$$x>-2$$
$$x<-1$$
Correct answer: $$x>-1$$
$$y<-5$$
Q5.
Use the graph to solve $$-5<x+1<-4x-9$$.
An image in a quiz
Correct answer: $$-6<x<-2$$
$$-6<x<-1$$
$$-2<x<-1$$
There is no solution to this inequality.
Q6.
Use the graph to solve $$-5<-4x-9<x+1$$.
An image in a quiz
$$-6<x<-2$$
$$-6<x<-1$$
Correct answer: $$-2<x<-1$$
There is no solution to this inequality.