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# "Exploring Inequalities and Their Graphs"  In this article, we delve into the topic of inequalities, which are similar to equations but feature symbols such as "<" or ">". We'll use the example of "x

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PowerPoint presentation about '"Exploring Inequalities and Their Graphs"'. This presentation describes the topic on In this article, we delve into the topic of inequalities, which are similar to equations but feature symbols such as "<" or ">". We'll use the example of "x. The key topics included in this slideshow are . Download this presentation absolutely free.

## Presentation Transcript

Slide1Solving Inequalities3-1 Exploring Inequalities and Their Graphs

Slide2An inequality  is like an equation, but instead of an equal sign (=) it has one of these signs: <    :  less than ≤   :  less than or equal to >   :  greater than ≥   :  greater than or equal to

Slide3“x < 5”means that whatever value  x has, it must be less than 5. Try to name ten numbers that are less than 5!

Slide4Numbers less than 5 are to the left of 5 on the number line. 0 5 10 15 -20 -15 -10 -5 -25 20 25 •   If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right. •  There are also numbers in between the integers, like 2.5, 1/2, - 7.9, etc. • The number 5 would  not  be a correct answer, though, because 5 is not less than 5. • Because 5 is not part of the answer, we use an OPEN dot to represent when the number is not included.

Slide5“x ≥ -2”means that whatever value  x has, it must be greater than  or equal to -2. Try to name ten numbers that are greater than or equal to -2!

Slide6Numbers greater than -2 are to theright  of -2 on the number line. 0 1 2 3 -4 -3 -2 -1 -5 4 5 •   If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right. •  There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5,  etc • The number -2  would also  be a correct answer, because of the phrase, “or equal to”. • Because -2 is part of the answer, we use a CLOSED dot to represent when the number is included.

Slide7Where is -1.5 on the number line?Is it greater or less than -2? 0 1 2 3 -4 -3 -2 -1 -5 4 5 •  -1.5 is between -1 and -2. •  -1 is to the right of -2. •  So -1.5 GREATER than -2.

Slide8Solve an Inequality – Preview Tomorroww + 5 < 8 We will use the same steps that we did with equations, if a number is added to the variable, we add the opposite sign to both sides: w + 5 +  (-5)  < 8 +  (-5) w < 3 All numbers less than 3 are solutions to this problem!

Slide9Today’s SummaryWhy Graph Inequalities? Because there is more than one answer! If the answer IS equal to..Closed Dot If the answer ISN’T equal to...Open Dot