CHAPTER 1 – EQUATIONS AND INEQUALITIES 1.3 – SOLVING EQUATIONS Unit 1 – First-Degree Equations and Inequalities

1.3 – Solving Equations In this section we will review:  Translating verbal expressions into algebraic expressions and equations, and vice versa  Solving equations using the properties of equality

1.3 – Solving Equations Real Numbers – Numbers that you use in everyday life  Real numbers can be either rational or irrational Rational number – can be expressed as a ratio m/n, where m and n are integers and n is not zero.  The decimal form is either terminating or repeating  Ex. 1/6, 1.9, …, -3, √4, 0

1.3 – Solving Equations Example 1  Write an algebraic expression to represent each verbal expression  The sum of a number and 10  The square of a number decreased by five times the cube of the same number

1.3 – Solving Equations Open sentence – A mathematical sentence containing one or more variables Equation – A mathematical sentence stating that two mathematical expression are equal

1.3 – Solving Equations Example 2  Write a verbal sentence to represent ech equations  15 = 20 – 5  p + (-6) = -11

1.3 – Solving Equations Open sentences are neither true nor false until the variables have been replaced by numbers Solution – A replacement that results in a true sentence

1.3 – Solving Equations PropertySymbolsExamples ReflexiveFor any real number a, a = a-7 + n = -7 + n SymmetricFor all real numbers a and b, if a = b then b = a If 3 = 5x – 6, then 5x – 6 = 3 TransitiveFor all real numbers a, b, and c, if a = b and b = c, then a = c If 2x + 1 = 7 and 7 = 5x – 8, then 2x + 1 = 5x - 8 SubstitutionIf a = b, then a may be replaced by b and b may be replaced by a If (4 + 5)m = 18, then 9m = 18

1.3 – Solving Equations Example 3  Name the property illustrated by each statement  z – n = z – n  (-7 + 2) · c = 35, then -5c = 35

1.3 – Solving Equations Sometimes you can solve an equation by adding, subtracting, multiplying, or dividing each side by the same number  Addition and Subtraction  For any real numbers a, b, and c, if a = b, then a + c = b + c, and a - c = b - c Ex. If x – 4 = 5, then x – = Ex. If n + 3 = -11, then n + 3 – 3 = -11 – 3  Multiplication and Division  For any real numbers a, b, and c, if a = b then a · c = b · c, and if c ≠ 0, a ÷ c = b ÷ c Ex. If m/4 = 6, then m/4 · 4 = 6 · 4 Ex. If -3y = 6, then -3y ÷ -3 = 6 ÷ -3

1.3 – Solving Equations Example 4  Solve each equation. Check your solution  g – 2.4 = 3.6  9/8n = -81

1.3 – Solving Equations Example 5  Solve -3(5a + 4) + 7(3a – 1) = -43

1.3 – Solving Equations Example 6  To find the amount of money in a savings account use the formula A = p + prt. In this formula, A is the amount in the savings account, p is the principle which is the original amount deposited in the account, r is the rate of interest, and t is the time. Solve the formula for t.

1.3 – Solving Equations Example 7  If 2x = -17/2, what is the value of 4/3x?  A. -17/6 B. -51/4 C. -17/3 D. -51/8

1.3 – Solving Equations Example 8  Several nurseries donated 1350 flower plants to be used in a new city park. A group of volunteers would like to plant 6 gardens each containing 72 of the plants and then use the remainder of the flowers in large pots that will hold 18 plants each. How many pots will be needed for the flowers?

1.3 – Solving Equations HOMEWORK Page 23 #31 – 41 odd, 53 – 57 odd, 58 – 63 all 1.1 – 1.3 Worksheet