2.1 Use the language of algebra  (Page 2/8)

When two quantities have the same value, we say they are equal and connect them with an equal sign .

An inequality is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that $b$ is greater than $a,$ it means that $b$ is to the right of $a$ on the number line. We use the symbols $\text{“<”}$ and $\text{“>”}$ for inequalities.

Inequality

$a<b$ is read $a$ is less than $b$

$a$ is to the left of $b$ on the number line

$a>b$ is read $a$ is greater than $b$

$a$ is to the right of $b$ on the number line

The expressions $a<b\text{and}a>b$ can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,

When we write an inequality symbol with a line under it, such as $a\le b,$ it means $a<b$ or $a=b.$ We read this $a$ is less than or equal to $b.$ Also, if we put a slash through an equal sign, $\text{≠,}$ it means not equal.

We summarize the symbols of equality and inequality in [link] .

The information in [link] compares the fuel economy in miles-per-gallon (mpg) of several cars. Write the appropriate symbol $\text{=},\text{<},\text{or}\text{>}$ in each expression to compare the fuel economy of the cars.

1. ⓐ MPG of Prius_____ MPG of Mini Cooper
2. ⓑ MPG of Versa_____ MPG of Fit
3. ⓒ MPG of Mini Cooper_____ MPG of Fit
4. ⓓ MPG of Corolla_____ MPG of Versa
5. ⓔ MPG of Corolla_____ MPG of Prius

Solution

ⓐ
	MPG of Prius____MPG of Mini Cooper
Find the values in the chart.	48____27
Compare.	48>27
	MPG of Prius>MPG of Mini Cooper

ⓑ
	MPG of Versa____MPG of Fit
Find the values in the chart.	26____27
Compare.	26<27
	MPG of Versa<MPG of Fit

ⓒ
	MPG of Mini Cooper____MPG of Fit
Find the values in the chart.	27____27
Compare.	27 = 27
	MPG of Mini Cooper = MPG of Fit

ⓓ
	MPG of Corolla____MPG of Versa
Find the values in the chart.	28____26
Compare.	28>26
	Corolla>MPG of Versa

ⓔ
	MPG of Corolla____MPG of Prius
Find the values in the chart.	28____48
Compare.	28<48
	MPG of Corolla<MPG of Prius

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