Linear Equations
Common Core Standard: Solve linear equations in one variable.
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Linear equations are equations of straight lines
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A variable is an unknown number that mathematician represent with a letter
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Like terms- are numbers that are the same variable or that have no variable
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Unless numbers are like terms they cannot be added or subtracted
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Constants are numbers that do not have a variable, because they stay the same or constant and variables change
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Inverse operations- are operations that undo each other; i.e., addition and subtraction & multiplication and division
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Example: 3z + -6 + 4z + 1 = 16
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The like terms are 3z and 4z, because they have the same variable
-6, 1, and 14 are also like terms they are the constants
Remember the add and subtract signs go with the numbers right after them
So, 3z + 4z = 7z
-6 + 1 = -5
Don’t do anything with the 16 yet, because it’s on the other side of the equation
7z - 5 = 16, now move the 5 over with the 16, because they are like terms by doing inverse operations
7z -5 + 5 = 16 + 5, since -5 + 5 equals zero we are able to successfully more the 5 with the 16
7z = 21, there are not anymore like terms, so to determine the variable, there must be only one of them,
currently there are 7
To get from 7z to 1z or z, divide 7 by 7, because that equals one, also it is the inverse operation
To keep the equation equal, divide both the 7z and the 21 by 7
Thus, z = 3
To prove this is true, we can put 3 in for z 3(3) + - 6 + 4(3) + 1 = 9 + -6 + 12 + 1 = 3 + 12 + 1 = 16
Example: 4h – 8 + 4 + -6h = 10
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The like terms are 4h and -6h; -8, 4, and 10 are the constants
4h + -6h = -2h
-8 + 4 = -4, leave 10 alone as it’s on the opposite side of the equations
-2h – 4 = 10, add 4 to both sides as 4 and 10 are like terms
-2h – 4 + 4 = 10 + 4 = -2h = 14
Now, divide both sides by -2, to get just 1h
-2h -2 = 14 ÷-2 = h = -7