How to Translate to an Equation and Solve
Translate to an Equation and Solve
In the past several examples, we were given an equation containing a variable. In the next few examples, we’ll have to first translate word sentences into equations with variables and then we will solve the equations.
Example
Translate and solve: five more than \(x\) is equal to \(-3.\)
Solution
| five more than \(x\) is equal to \(-3\) | |
| Translate | \(x+5=-3\) |
| Subtract \(5\) from both sides. | \(x+5-5=-3-5\) |
| Simplify. | \(x=\mathrm{-8}\) |
Check the answer by substituting it into the original equation.
\(\begin{array}{}\\ \\ \hfill x+5=-3\phantom{\rule{1.35em}{0ex}}\\ \hfill -8+5\stackrel{?}{=}-3\phantom{\rule{1.35em}{0ex}}\\ \hfill -3=-3✓\end{array}\)
Example
Translate and solve: the difference of \(n\) and \(6\) is \(-10.\)
Solution
| the difference of \(n\) and \(6\) is \(-10\) | |
| Translate. | \(n-6=-10\) |
| Add \(6\) to each side. | \(n-6+6=-10+6\) |
| Simplify. | \(n=-4\) |
Check the answer by substituting it into the original equation.
\(\begin{array}{}\\ \hfill \phantom{\rule{0.5em}{0ex}}n-6=-10\phantom{\rule{1.35em}{0ex}}\\ \hfill -4-6\stackrel{?}{=}-10\phantom{\rule{1.35em}{0ex}}\\ \hfill -10=-10✓\end{array}\)
Example
Translate and solve: the number \(108\) is the product of \(-9\) and \(y.\)
Solution
| the number of \(108\) is the product of \(-9\) and \(y\) | |
| Translate. | \(108=-9y\) |
| Divide by \(-9\). | \(\frac{108}{-9}=\frac{-9y}{-9}\) |
| Simplify. | \(-12=y\) |
Check the answer by substituting it into the original equation.
\(\begin{array}{c}108=-9y\hfill \\ 108\stackrel{?}{=}-9\left(-12\right)\hfill \\ 108=108✓\hfill \end{array}\)
This lesson is part of:
Introducing Integers