1) GOAL : Get the variable on one side of the equation. 2) You always perform the same operation to both sides of an equation. 3) To undo an operation you perform its opposite operation to both sides of the equation.

The inverse of add is SUBTRACT The inverse of subtract is ADD The inverse of multiply is The inverse of divide is DIVIDE MULTIPLY

What you do to one side of an equation, you must do to the other side to keep it balanced x 6 =

To solve a multiplication equation Use the inverse operation for multiplication which is division. Get the variable alone, by dividing the same number into both sides.

Try to solve this multiplication equation. 56 8x = How do you get x all by itself?

56 8x = Divide 8 into both sides

56 8x = Divide 8 into both sides. 7 Check your answer by substitution!

Try to solve this multiplication equation 42 7x = How do you get x all by itself?

42 7x = 77 6 Divide 7 into both sides.

42 7x = 6 Divide 7 into both sides. Check your answer by substitution!

To Solve a Multiplication Equation 8x = 32 Get the variable alone. 8 8 Divide 8 into both sides. x = 4 8 divided by 8 cancels out 8 4 = 32 Show your check! Divide the same number into both sides 32 = 32 Finish your check!

1) 2) 3) 4)

To solve a division equation Use the inverse operation for division which is multiplication. Get the variable alone, by multiplying the same number to both sides.

Try to solve this division equation x3x3 15 = How do you get x all by itself?

x3x3 15 = 3 3 Multiply both sides by 3 45

x3x3 15 = Multiply both sides by 3 45 Check your answer by substitution!

Try to solve this division equation x6x6 4 = How do you get x all by itself?

x6x6 4 = 6 6 Multiply both sides by 6 24

x6x6 4 = Multiply both sides by 6 24 Check your answer by substitution!

Try to solve this division equation x7x7 -7 = How do you get x all by itself?

x7x7 -7 = 7 7 Multiply both sides by 7 -49

x7x7 -7 = Multiply both sides by Check your answer by substitution!

To Solve a Division Equation Multiply the same number to both sides. = 25 Get the variable alone. = 25 Multiply both sides by 3. x = 75 3 divided by 3 cancels out to 1. Show your check! x3x3 x3x3 25 = 25 Finish your check! 3 3

-3x = x = -7 m = 8 -2 (-2) m = (-7) = = 21 8 = 8 Try These Equations Show your check!

Try These Equations 1)2)

Try These Equations 3)4)

Take Out Your Study Guide!!!

5x = 40 Get the variable alone. 5 5 Divide 5 into both sides. x = 8 5 divided by 5 cancels out to = 40 Show your check! Divide the same number into both sides #5 40 = 40 Finish your check!

= 20 Get the variable alone. = 20 Multiply both sides by 2. x = 40 2 divided by 2 cancels out to 1. Show your check! x2x2 x2x2 Multiply the same number to both sides #6 20 = 20 Finish your check! 2 2

Add plus sum increased by total more than added to Subtract minus difference decreased by less than subtracted from less Multiply times product of twice Divide quotient Flip Flop Numbers

Placement Rule Always write the variable after the number! a 4 WRITE IT AS 4a

Using Parentheses 8 x is written as 8(x) (8)x (8x) 8x Parentheses mean multiply!

Translate the following into equations. 1) Eleven more than a number t is 23. 2) Eight times a number k is equal to 56. 3) Thirteen less m equals 6. 4) The quotient of x and 3 is 18.

Four times the sum of m and 5 minus 3 Five minus twice the quotient of x and 8 The quotient of a and 7 minus 3 Write a phrase that describes each variable expression below.

Long Way Short Way Easier to multiply by the reciprocal!

Solve the division by multiplying by the reciprocal.

Solve the division by multiplying by the reciprocal.

Solve the division by multiplying by the reciprocal.

#7 Multiply both sides by the reciprocal of the fraction. Multiply the numerators. Multiply the denominators. Simplify

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