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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

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

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Lesson details

Key learning points

By comparing the graphs to the algebraic approach, you can compare the representations of the solution set
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.

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

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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.

$$(4,-2)$$ is the point of of these two linear graphs.

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?

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?

$$-2\le{y}\le4$$

$$-2<{y}<4$$

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 $$x>-2$$.

Correct answer: solution to

intersection of

equation for

Q2.

This graph shows that the region $$x<4$$ is the solution to which inequality?

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 $$x+1<2x-3$$.

$$x<4$$

Correct answer: $$x>4$$

$$x<-1$$

$$x>-1$$

$$x>-2$$

Q4.

Use the graph to solve $$-4x-9<2x-3$$.

$$x<-2$$

$$x>-2$$

$$x<-1$$

Correct answer: $$x>-1$$

$$y<-5$$

Q5.

Use the graph to solve $$-5<x+1<-4x-9$$.

Correct answer: $$-6<x<-2$$

$$-6<x<-1$$

$$-2<x<-1$$

There is no solution to this inequality.

Q6.

Use the graph to solve $$-5<-4x-9<x+1$$.

$$-6<x<-2$$

$$-6<x<-1$$

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

There is no solution to this inequality.