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

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Translate from algebra to words.

ⓐ $47 - 19$
ⓑ $72 \div 9$
ⓒ $m + n$
ⓓ $(13) (7)$

ⓐ 47 minus 19; the difference of forty-seven and nineteen
ⓑ 72 divided by 9; the quotient of seventy-two and nine
ⓒ m plus n ; the sum of m and n
ⓓ 13 times 7; the product of thirteen and seven

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

Equality symbol

$a = b is read a is equal to b$

The symbol $=$ is called the 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 $“<”$ and $“>”$ for inequalities.

Inequality

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

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

The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.

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

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

The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.

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

\begin{array}{l} a < b is equivalent to b > a . For example, 7 < 11 is equivalent to 11 > 7 . \\ a > b is equivalent to b < a . For example, 17 > 4 is equivalent to 4 < 17 . \end{array}

When we write an inequality symbol with a line under it, such as $a \leq b,$ 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, $≠,$ it means not equal.

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

Algebraic Notation	Say
$a = b$	$a$ is equal to $b$
$a \neq b$	$a$ is not equal to $b$
$a < b$	$a$ is less than $b$
$a > b$	$a$ is greater than $b$
$a \leq b$	$a$ is less than or equal to $b$
$a \geq b$	$a$ is greater than or equal to $b$

Symbols $<$ And $>$

The symbols $<$ and $>$ each have a smaller side and a larger side.

smaller side $<$ larger side
larger side $>$ smaller side

The smaller side of the symbol faces the smaller number and the larger faces the larger number.

Translate from algebra to words:

ⓐ $20 \leq 35$
ⓑ $11 \neq 15 - 3$
ⓒ $9 > 10 \div 2$
ⓓ $x + 2 < 10$

Solution

ⓐ

20 \leq 35

20 is less than or equal to 35

ⓑ

11 \neq 15 - 3

11 is not equal to 15 minus 3

ⓒ

9 > 10 \div 2

9 is greater than 10 divided by 2

ⓓ

x + 2 < 10

x

plus 2 is less than 10

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Translate from algebra to words.

ⓐ $14 \leq 27$
ⓑ $19 - 2 \neq 8$
ⓒ $12 > 4 \div 2$
ⓓ $x - 7 < 1$

ⓐ fourteen is less than or equal to twenty-seven
ⓑ nineteen minus two is not equal to eight
ⓒ twelve is greater than four divided by two
ⓓ x minus seven is less than one

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Translate from algebra to words.

ⓐ $19 \geq 15$
ⓑ $7 = 12 - 5$
ⓒ $15 \div 3 < 8$
ⓓ $y + 3 > 6$

ⓐ nineteen is greater than or equal to fifteen
ⓑ seven is equal to twelve minus five
ⓒ fifteen divided by three is less than eight
ⓓ y minus three is greater than six

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

This table has two rows and six columns. The first column is a header column and it labels each row The first row is labeled “Car” and the second “Fuel economy (mpg)”. To the right of the ‘Car’ row are the labels: “Prius”, “Mini Cooper”, “Toyota Corolla”, “Versa”, “Honda Fit”. Each of these columns contains an image of the labeled car model. To the right of the “Fuel economy (mpg)” row are the algebraic equations: the letter p, the equals symbol, the number forty-eight; the letter m, the equals symbol, the number twenty-seven; the letter c, the equals symbol, the number twenty-eight; the letter v, the equals symbol, the number twenty-six; and the letter f, the equals symbol, the number twenty-seven. — (credit: modification of work by Bernard Goldbach, Wikimedia Commons)

ⓐ MPG of Prius_____ MPG of Mini Cooper
ⓑ MPG of Versa_____ MPG of Fit
ⓒ MPG of Mini Cooper_____ MPG of Fit
ⓓ MPG of Corolla_____ MPG of Versa
ⓔ 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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Source: OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9

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

Equality symbol

Inequality

Symbols < And >

Solution

Solution

Questions & Answers

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Symbols $<$ And $>$