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.
  1. Locate the “equals” word(s). Translate to an equals sign (=).
  2. Translate the words to the left of the “equals” word(s) into an algebraic expression.
  3. 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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