Chapter 3 – Solving Linear Equations 3.2 – Solving Equations Using Multiplication and Division

Today we will learn how to: Today we will learn how to: Solve linear equations using multiplication and division Solve linear equations using multiplication and division Use multiplication and division equations to solve real-life and geometric problems Use multiplication and division equations to solve real-life and geometric problems

3.2 – Solving Equations Using Multiplication and Division Just like with adding and subtracting, we can solve equations using multiplication and division. Just like with adding and subtracting, we can solve equations using multiplication and division. The same rules apply: The same rules apply: If you are moving terms to the other side of the equal sign, do the inverse operation If you are moving terms to the other side of the equal sign, do the inverse operation OPPOSITE SIDES = OPPOSITE OPERATION OPPOSITE SIDES = OPPOSITE OPERATION If the terms are on the same side of the equal sign, simplify If the terms are on the same side of the equal sign, simplify SAME SIDE = SIMPLIFY SAME SIDE = SIMPLIFY

3.2 – Solving Equations Using Multiplication and Division EQUIVALENT EQUATIONS EQUIVALENT EQUATIONS Multiply each side of the equation by the same nonzero number Multiply each side of the equation by the same nonzero number ORIGINAL: x  2 = 3 ORIGINAL: x  2 = 3 Multiply both sides by 2 Multiply both sides by 2 EQUIVALENT: x = 6 EQUIVALENT: x = 6 Divide each side of the equation by the same nonzero number Divide each side of the equation by the same nonzero number ORIGINAL: 4x = 12 ORIGINAL: 4x = 12 Divide both sides by 4 Divide both sides by 4 EQUIVALENT: x = 3 EQUIVALENT: x = 3

3.2 – Solving Equations Using Multiplication and Division Example 1 Example 1 Solve the following equations: Solve the following equations: -3x = 2 -3x = 2 x  9 = -25 x  9 = = (-7  8)m 14 = (-7  8)m

3.2 – Solving Equations Using Multiplication and Division PROPERTIES OF EQUALITY PROPERTIES OF EQUALITY ADDITION PROPERTY OF EQUALITY ADDITION PROPERTY OF EQUALITY If a = b, then a + c = b + c If a = b, then a + c = b + c SUBTRACTION PROPERTY OF EQUALITY SUBTRACTION PROPERTY OF EQUALITY If a = b, then a - c = b - c If a = b, then a - c = b - c MULTIPLICATON PROPERTY OF EQUALITY MULTIPLICATON PROPERTY OF EQUALITY If a = b, then ac = bc If a = b, then ac = bc DIVISION PROPERTY OF EQUALITY DIVISION PROPERTY OF EQUALITY If a = b and c ≠ 0, then a /c = b /c If a = b and c ≠ 0, then a /c = b /c

3.2 – Solving Equations Using Multiplication and Division Example 2 Example 2 A time-lapse camera photographed a growing plant at the rate of 25 frames per hour over several weeks. For how many days was the plant photographed if there were a total of 17,400 frames? A time-lapse camera photographed a growing plant at the rate of 25 frames per hour over several weeks. For how many days was the plant photographed if there were a total of 17,400 frames?

3.2 – Solving Equations Using Multiplication and Division HOMEWORK Page 142 #24 – 46 even, 49 – 52