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, 2.575757…, -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Open sentences are neither true nor false until the variables have been replaced by numbers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

Property Symbols Examples

Reflexive For any real number a, a = a

-7 + n = -7 + n

Symmetric For all real numbers a and b, if a = b then b = a

If 3 = 5x – 6, then 5x – 6 = 3

Transitive For 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

Substitution If 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 – 4 + 4 = 5 + 4 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

HOMEWORKPage 23

#31 – 41 odd, 53 – 57 odd, 58 – 63 all

1.1 – 1.3 Worksheet