Solving Equations Using the Division Property of Equality
Solving Equations Using the Division Property of Equality
The previous examples lead to the Division Property of Equality. When you divide both sides of an equation by any nonzero number, you still have equality.
Division Property of Equality
\(\text{For any numbers a, b, c, and } \mathrm{c≠0},\)
\(\mathrm{If \; a = b, \; then \;} \frac{a}{c} = \frac{b}{c}.\)
Example
\(\text{Solve:}\phantom{\rule{0.2em}{0ex}}7x=-49.\)
Solution
To isolate \(x,\) we need to undo multiplication.
| Divide each side by 7. | |
| Simplify. |
Check the solution.
| \(7x=-49\phantom{\rule{1.35em}{0ex}}\) | |
| Substitute −7 for x. | \(7\left(-7\right)\stackrel{?}{=}-49\phantom{\rule{1.35em}{0ex}}\) |
| \(-49=-49✓\) |
Therefore, \(-7\) is the solution to the equation.
Example
Solve: \(-3y=63.\)
Solution
To isolate \(y,\) we need to undo the multiplication.
| Divide each side by −3. | |
| Simplify |
Check the solution.
| \(-3y=63\phantom{\rule{1.35em}{0ex}}\) | |
| Substitute −21 for y. | \(-3\left(-21\right)\stackrel{?}{=}63\phantom{\rule{1.35em}{0ex}}\) |
| \(63=63✓\) |
Since this is a true statement, \(y=-21\) is the solution to the equation.
Optional Video: One-Step Equations With Multiplying Or Dividing
This lesson is part of:
Introducing Integers
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