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The expressions a <b or a> b can be read from left to right or right to left, though in English we usually read from left to right ( [link] ). In general, a <b is equivalent to b> a . For example 7<11 is equivalent to 11>7. And a > b is equivalent to b <a. For example 17>4 is equivalent to 4<17.
| Inequality Symbols | Words |
|---|---|
| a is not equal to b | |
| a < b | a is less than b |
| a is less than or equal to b | |
| a>b | a is greater than b |
| a is greater than or equal to b |
Translate from algebra into English:
ⓐ ⓑ ⓒ ⓓ
ⓐ
17 is less than or equal to 26
ⓑ
8 is not equal to 17 minus 3
ⓒ
12 is greater than 27 divided by 3
ⓓ
y plus 7 is less than 19
Translate from algebra into English:
ⓐ ⓑ ⓒ ⓓ
ⓐ 14 is less than or equal to 27 ⓑ 19 minus 2 is not equal to 8 ⓒ 12 is greater than 4 divided by 2 ⓓ x minus 7 is less than 1
Translate from algebra into English:
ⓐ ⓑ ⓒ ⓓ
ⓐ 19 is greater than or equal to 15 ⓑ 7 is equal to 12 minus 5 ⓒ 15 divided by 3 is less than 8 ⓓ y plus 3 is greater than 6
Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in English. They help to make clear which expressions are to be kept together and separate from other expressions. We will introduce three types now.
Here are some examples of expressions that include grouping symbols . We will simplify expressions like these later in this section.
What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. “Running very fast” is a phrase, but “The football player was running very fast” is a sentence. A sentence has a subject and a verb. In algebra, we have expressions and equations .
An expression is a number, a variable, or a combination of numbers and variables using operation symbols.
An expression is like an English phrase. Here are some examples of expressions:
| Expression | Words | English Phrase |
|---|---|---|
| 3 plus 5 | the sum of three and five | |
| n minus one | the difference of n and one | |
| 6 times 7 | the product of six and seven | |
| x divided by y | the quotient of x and y |
Notice that the English phrases do not form a complete sentence because the phrase does not have a verb.
An equation is two expressions linked with an equal sign . When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb.
An equation is two expressions connected by an equal sign.
Here are some examples of equations.
| Equation | English Sentence |
|---|---|
| The sum of three and five is equal to eight. | |
| n minus one equals fourteen. | |
| The product of six and seven is equal to forty-two. | |
| x is equal to fifty-three. | |
| y plus nine is equal to two y minus three. |
Determine if each is an expression or an equation:
ⓐ ⓑ ⓒ ⓓ
ⓐ
ⓑ
ⓒ
ⓓ
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