Relating graphical solutions to algebraic solutions for inequalities | Maths

Starter quiz

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

'intersection' ✓
Solve $5x-7\geq{2x+38}$ .

$x\geq15$ ✓

$x>15$

$x\le15$

$x<15$

$x=15$
Which inequality is represented by this region?

$x>-4$ ✓

$x<-4$

$x=-4$

$x\le-4$

$x\geq-4$
Solve ${x+8}<{2x+14}\le{6}$ .

$-6$

$-6$

$-6\le{x}<-4$

$-6 ✓$

$x\le-4$
Which inequality is represented by this region?

$-2\le{y}\le4$

$-2<{y}<4$

$-2<{y}\le4$ ✓

$-2<{x}\le4$

$4<{y}\le-2$
Solve ${1-3x}>10$ .

$x<-3$ ✓

$x>-3$

$x<3$

$x>3$

Exit quiz

This graph shows us that the __________ $2x+8>2-x$ is $x>-2$ .

solution to ✓

intersection of

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

$2x-3 ✓$

$2x-3>x+1$

$2x-3\le{x+1}$

$2x-3\geq{x+1}$
Use the graph to solve $x+1<2x-3$ .

$x<4$

$x>4$ ✓

$x<-1$

$x>-1$

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

$x<-2$

$x>-2$

$x<-1$

$x>-1$ ✓

$y<-5$
Use the graph to solve $-5 .$

$-6 ✓$

$-6$

$-2$

There is no solution to this inequality.
Use the graph to solve $-5<-4x-9 .$

$-6$

$-6$

$-2 ✓$

There is no solution to this inequality.

Worksheet

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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

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.

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.