Algebra 1: Chapter 1, Lesson 7, page 33.
Solving Equations, An Introduction
An EQUATION is a mathematical sentence that uses the equal sign `=` to state that 2 expressions represent the same number or are equivalent. An equation that contains at least 1 variable is called an OPEN SENTENCE.
The set of numbers from which you can select replacements for the variable is called the REPLACEMENT SET, usually noted with squiggly brackets `{2, 5, 12}`. A replacement for a variable that makes an equation true is called the SOLUTION. To SOLVE and equation means to find all of its solutions. The collection of all the solutions is called the SOLUTION SET, usually contained in the { brackets}.
2 equations are EQUIVALENT if one can be obtained from the other by a sequence of the following steps. You can:
- add the same number to both sides of an equation
- subtract the same number from both sides of an equation
- multiply both sides of an equation by the same number
- divide both sides of an equation by the same number
Equivalent equations have the same solutions set.
Two of tonight’s homework problems solved by MrE are here! Just click it!!
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Algebra 1a: Chapter 1, Lesson 4, page 19.
The Associative Property
We discussed the use of the Associative property by re-grouping terms in paranthesis. We also used both commutative and associative properties together to help simplify expressions for evaluation.
We looked for patterns in expressions again to help speed up our mental math computation speed.
Remember, the associative property ONLY holds true for addition and multiplication. Just like the commutative property, it doesn’t work for subtraction or division.
For any numbers a, b, and c, we have in equation forms for adding and multiplication:
`a+(b+c)=(a+b)+c and a⋅(b⋅c)=(a⋅b)⋅c`
Two of tonight’s homework problems solved by MrE are here! Just click it!!