Ch 3.1 Objective: To solve simple, one-step variable equations

Definition Equation A balanced statement of equality between two quantities. One Step Only one operation is performed (+, -, *, ÷) = 7 fulcrum =

1) Goal: Isolate the variable. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation.

fulcrum = - 3

fulcrum 4 7 =

4 7 =

4 7 =

= - 3

44 = Perform the same operation to both sides to keep the equation balanced.

x = This property can be used to solve variable equations. -6 x5 = x + 6 = x = 5 Algebraic Approach

Solve. 1) m + 2 = 10 2) x - 4 = 6 3) x + 7 = 3 4) m - 4 = 9 5) 11 = x ) 8 + y = m = 8 +4 x = x = m = = x -8 y = -14

Solve. 1) -4 + x = 15 2) 7 = x ) -10 = 6 + x 4) - 4 = m + 9 5) = x 6) y = x = = x = x = m 16 = x y = -5

Solve. 1) 5x = 35 2) 3) 9 = -3m 4) 5 x = 7 (-6) -72 = x = m

Solving Equations Involving Fractions Long WayShort Way Easier to multiply by the reciprocal!

Solve. 1) 7x = 16 2) 3) 9 = -m 4) 7 (-2) k = 16 (-1)9 = -m(-1) -9 = m (-4)

Solve. 1) 2) 3) 4)

Acceptable Answers -4k = There is nothing improper about an improper fraction! All answers must be fully reduced!