example
Translate the sentence into an algebraic equation: The sum of [latex]6[/latex] and [latex]9[/latex] is [latex]15[/latex].
Solution
The word
is tells us the equal sign goes between 9 and 15.
Locate the "equals" word(s). |
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Write the = sign. |
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Translate the words to the left of the equals word into an algebraic expression. |
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Translate the words to the right of the equals word into an algebraic expression. |
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example
Translate the sentence into an algebraic equation: The product of [latex]8[/latex] and [latex]7[/latex] is [latex]56[/latex].
Answer:
Solution
The location of the word is tells us that the equal sign goes between 7 and 56.
Locate the "equals" word(s). |
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Write the = sign. |
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Translate the words to the left of the equals word into an algebraic expression. |
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Translate the words to the right of the equals word into an algebraic expression. |
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example
Translate the sentence into an algebraic equation: Twice the difference of [latex]x[/latex] and [latex]3[/latex] gives [latex]18[/latex].
Answer:
Solution
Locate the "equals" word(s). |
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Recognize the key words: twice; difference of …. and …. |
Twice means two times. |
Translate. |
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example
Translate and solve: Three more than [latex]x[/latex] is equal to [latex]47[/latex].
Answer:
Solution
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Three more than x is equal to [latex]47[/latex]. |
Translate. |
[latex]x+3=47[/latex] |
Subtract [latex]3[/latex] from both sides of the equation. |
[latex]x+3\color{red}{--3}=47\color{red}{--3}[/latex] |
Simplify. |
[latex]x=44[/latex] |
We can check. Let [latex]x=44[/latex] . |
[latex]x+3=47[/latex] |
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[latex]44+3=47[/latex] |
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[latex]47=47[/latex] |
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So [latex]x=\text{}44[/latex] is the solution.
example
Translate and solve: The difference of [latex]y[/latex] and [latex]14[/latex] is [latex]18[/latex].
Answer:
Solution
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The difference of y and [latex]14 is 18[/latex]. |
Translate. |
[latex]y--14=18[/latex] |
Add [latex]14[/latex] to both sides. |
[latex]y--14\color{red}{+14}=18\color{red}{+14}[/latex] |
Simplify. |
[latex]y=32[/latex] |
We can check. Let [latex]y=32[/latex] . |
[latex]y--14=18[/latex] |
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[latex]32--14=18[/latex] |
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[latex]18=18[/latex] |
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So [latex]y=32[/latex] is the solution.