Algebra 1 Unit 1 Mastery Test
These properties of equality help maintain balance in an equation when performing the same operation on both sides. Inverse operations, like using addition to undo subtraction, are key tools in solving equations.
Property of Equality
Add, subtract, multiply, or divide the same number on each side of the equal sign. Keep equation BALANCED!
Key Terms
Property of Equality
Add, subtract, multiply, or divide the same number on each side of the equal sign. Keep equation BALANCED!
Addition Property of Equality
If a = b, then a + c = b + c
Subtraction Property of Equality
If a = b, then a - c = b - c
Multiplication Property of Equality
If a = b and c ≠ 0, then a ⦁ c = b ⦁ c
Division Property of Equality
If a = b and c ≠ 0, then a ÷ c = b ÷ c
Inverse Operation
The opposite or reverse operation
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| Term | Definition |
|---|---|
Property of Equality | Add, subtract, multiply, or divide the same number on each side of the equal sign. Keep equation BALANCED! |
Addition Property of Equality | If a = b, then a + c = b + c |
Subtraction Property of Equality | If a = b, then a - c = b - c |
Multiplication Property of Equality | If a = b and c ≠ 0, then a ⦁ c = b ⦁ c |
Division Property of Equality | If a = b and c ≠ 0, then a ÷ c = b ÷ c |
Inverse Operation | The opposite or reverse operation |
Inverse Operation of SUBTRACTION | Addition |
Inverse Operation of ADDITION | Subtraction |
Inverse Operation of MULTIPLICAITON | Division |
Inverse Operation of DIVISION | Multiplication |
x+6=-4 | Given |
x+6. =-4 | Property of equality |
x+0=-10 | Inverse |
x=-10 | Identity |
Equation | a mathematical statement that two expressions are equal |
Solve | To find the solution |
Solution | Value that makes an equation true |
Inverse operations | operations that undo each other |
isolate the variable | To get a variable alone on one side of an equation or inequality in order to solve the equation or inequality |
Linear equations in one variable | An equation which an be written in the form ax+b=c |
Terms are separated by | addition and subtraction signs |
Like terms | terms with the same variable and exponent |
Coefficient | Numerical part of term |
How can coefficient if like terms be combined | By adding or subtracting |
Constant | a number with no variable |
Identity | All real solutions x+1=x+1 |
Conditional | X = # , equation that is true for some values 2x-5=9 only true for x=7 |
Contradiction | Empty set , no solution x+1=x+2 |
What is an equation that is false for every solution | A contradiction |