Translating to An Equation and Solving
Translating to An Equation and Solving
To solve applications algebraically, we will begin by translating from English sentences into equations. Our first step is to look for the word (or words) that would translate to the equals sign. The table below shows us some of the words that are commonly used.
| Equals = |
|---|
| is is equal to is the same as the result is gives was will be |
The steps we use to translate a sentence into an equation are listed below.
Translate an English sentence to an algebraic equation.
- Locate the “equals” word(s). Translate to an equals sign (=).
- Translate the words to the left of the “equals” word(s) into an algebraic expression.
- Translate the words to the right of the “equals” word(s) into an algebraic expression.
Example
Translate and solve: Eleven more than x is equal to 54.
Solution
| Translate. | |
| Subtract 11 from both sides. | |
| Simplify. | |
| Check: Is 54 eleven more than 43? \(\begin{array}{ccc}\hfill 43+11& \stackrel{?}{=}\hfill & 54\hfill \\ \hfill 54& =\hfill & 54✓\hfill \end{array}\) |
Example
Translate and solve: The difference of \(12t\) and \(11t\) is \(-14\).
Solution
| Translate. | |
| Simplify. | |
| Check: \(\begin{array}{ccc}\hfill 12\left(-14\right)-11\left(-14\right)& \stackrel{?}{=}\hfill & -14\hfill \\ \hfill -168+154& \stackrel{?}{=}\hfill & -14\hfill \\ \hfill -14& =\hfill & -14✓\hfill \end{array}\) |
This lesson is part of:
Solving Linear Equations II
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