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Mathematics » Introducing Integers » Solve Equations Using Integers; The Division Property of Equality

# Key Concepts

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## Key Concepts

• How to determine whether a number is a solution to an equation.
• Step 1. Substitute the number for the variable in the equation.
• Step 2. Simplify the expressions on both sides of the equation.
• Step 3. Determine whether the resulting equation is true.
• If it is true, the number is a solution.
• If it is not true, the number is not a solution.
• Properties of Equalities
Subtraction Property of EqualityAddition Property of Equality
$$\text{For any numbers}\phantom{\rule{0.2em}{0ex}}a,b,c,$$

$$\text{if}\phantom{\rule{0.2em}{0ex}}a=b\phantom{\rule{0.2em}{0ex}}\text{then}\phantom{\rule{0.2em}{0ex}}a-c=b-c.$$

$$\text{For any numbers}\phantom{\rule{0.2em}{0ex}}a,b,c,$$

$$\text{if}\phantom{\rule{0.2em}{0ex}}a=b\phantom{\rule{0.2em}{0ex}}\text{then}\phantom{\rule{0.2em}{0ex}}a+c=b+c.$$

• Division Property of Equality
• For any numbers $$a,b,c,$$ and $$c\ne 0$$

If $$a=b$$, then $$\frac{a}{c}=\frac{b}{c}$$.