Lesson 2-2

Undo the addition by subtracting 3 from each side 2x + 3 – 3 = 15 – 3 Simplify 2x = 12 A. Solve 2x + 3 = 15 Undo the multiplication by dividing each side by 2. x = 6 Simplify NOTE: You can check your solution by replacing the variable in the original equation and seeing if both sides are equal.

B.You are making a bulleting board to advertise community service opportunities in your town. You plan to use a half sheet of construction paper for each ad. You need 5 sheets of construction paper for a title banner. You have 18 sheets of construction paper. How many ads can you make? Know: Have 18 sheets Need 5 sheets for title banner Need ½ sheet for each add Sketch:

Define the variable : Let ____ = _______________ a# of ads Write an equation:________________________ Undo add/subtraction: ________________________ (use the inverse operation) Simplify: ________________________ Undo mult/.division________________________ ( use the inverse operation or multiply by the reciprocal) Simplify:________________________ ½ a + 5 = 18 ½ a + 5 – 5 = 18 – 5 ½ a = 13 (2) ● (½ a) = 13 ● (2) a = 26

SOLVING WITH TWO TERMS IN THE NUMERATOR: C. Multiply each side by the denominator. (Use a LCD if there is more than one denominator.) This eliminates the fraction. r – 8 = 6 Simplify r – = Undo the addition/subtraction using the inverse operation. r = 14 Simplify

Work these problems on your own. You can check your answers on the last screen. (You must show your work.)

Using Deductive Reasoning: When you use deductive reasoning, you must state the steps and your reason for each step using _______________, definitions, and rules. properties D. What is the solution of – t + 8 = 3? Justify each step. Given Subtraction Property of Equality Substitution Identity Property for Multiplication Division Property of Equality Substitution

E. What properties of equality would you use to solve the equation? s = – 44 Given Symmetric Property Subtraction Property of Equality Multiplication Property of Equality Simplify

Work these problems on your own. You can check your answers on the last screen. (You must show your work.)

Solutions to practice problems: 1.x = – 5 2.m = 63 3.y = – 7 4.x = 13 5.Each granola bar costs $0.62 (or 62¢ each) 6.x = 8 Reasons: GIVEN, Addition Property of Equality, Substitution, Division Property of Equality, Substitution 7.x = 36 Reasons: Given, Addition Property of Equality, Substitution, Division Property of Equality, substitution