Graphing inequalities review

Google Classroom

Review graphing inequalities with variables on number lines, and then try some practice problems.

Inequalities

Inequalities show the relation between two expressions that are not equal.

Below are some examples of inequalities:

$9>7$9, is greater than, 7

$6\ \underline< \ a+2$6, space, start underline, is less than, end underline, space, a, plus, 2

$x<5$x, is less than, 5

Inequalities symbols

Symbol	Meaning
$>$is greater than	Greater than
$\underline>$start underline, is greater than, end underline	Greater than or equal to
$<$is less than	Less than
$\underline<$start underline, is less than, end underline	Less than or equal to

Graphing inequalities with variables

We can use a number line to show the possible solutions to an inequality.

Example 1: $x>4$x, is greater than, 4

An inequality like $x>4$x, is greater than, 4 tells us that $x$x can be any value greater than $4$4.

We can show this on a number line by putting an open circle on $4$4 and shading the numbers that are greater than $4$4.

$\llap{-}5$$\llap{-}4$$\llap{-}3$$\llap{-}2$$\llap{-}1$$0$$1$$2$$3$$4$$5$

Example 2: $y\ \underline<\ 3$y, space, start underline, is less than, end underline, space, 3

If we have either the $\underline>$start underline, is greater than, end underline or $\underline<$start underline, is less than, end underline symbol in our inequality, we shade in the circle to show that the variable may be equal to that number.

For example, $y\ \underline<\ 3$y, space, start underline, is less than, end underline, space, 3 is graphed as follows:

$\llap{-}5$$\llap{-}4$$\llap{-}3$$\llap{-}2$$\llap{-}1$$0$$1$$2$$3$$4$$5$

This number line shows that $y$y is either equal to $3$3 or less than $3$3.

Want to learn more about graphing inequalities? Check out this video.