EQUATIONS REVIEW COMBINING LIKE TERMS A term can

EQUATIONS REVIEW

COMBINING LIKE TERMS A term can be a number, a variable, or a product of numbers and variables A coefficient is a number that is multiplied by a variable Like terms have the same variable and the same exponent Coefficients do not have to be the same Constants (numbers) are like terms

EXAMPLES Which terms are “like”? 5 x, 8 y, 9 z, 10, 12 x, 14 z, 7 Like: 5 x and 12 x Like: 10 and 7 Like: 9 z and 14 z

COMBINING LIKE TERMS Add or subtract the coefficients to combine like terms Take the symbol that is in front of the term 6 x 2 + 5 y + 7 x 2 – 3 y – 4 x 4 6 x 2 + 7 x 2 + 5 y – 3 y – 4 x 4 13 x 2 + 2 y – 4 x 4

ONE-STEP EQUATIONS To isolate the variable is to get the variable alone Use inverse operations to isolate the variable Think of these as “opposite” operations

ONE-STEP EQUATIONS Think of an equation as a balance (try to keep the sides equal) What you do to one side, you must do to the other

SOLVE: R + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

SOLVE: R + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

1. Draw “the river” to separate the equation into 2 sides 2. Subtract 16 from both sides 3. Simplify vertically 4. Check your answer by substituting your answer back into the problem R + 16 = -7 - 16 -16 r = -23 + 16 = -7

1. Draw “the river” to separate the equation into 2 sides 2. Subtract 2 from both sides 3. Simplify vertically 4. Check your answer by substituting your answer back into the problem X + 2 = -3 -2 -2 x = -5 -5 + 2 = -3 Be sure to check your work!!

TWO-STEP EQUATIONS Use inverse operations to isolate the variable, just like in a one-step equation, but follow order of operations in reverse Undo addition or subtraction first Then, undo multiplication or division

SOLVE: 4 X – 5 = 11 4 x – 5 = 15 +5 +5 (Add 5 to both sides) 4 x = 20 (Simplify) 4 4 (Divide both sides by 4) x=5 (Simplify)

MULTI-STEP EQUATIONS Combine like terms, if any. Use the distributive property, if necessary.

MULTI-STEP EQUATION -5 x + 21 + 7 x + 21 = -2

SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES Group the terms with variables on one side of the equal sign, and simplify.

Variables on Both Sides 6 x + 15 = 125 + 4 x (6 x – 4 x) + 12 = 122 + (4 x – 4 x) 2 x + 12= 122 -12 2 x = 110 2 2 X = 55