Section 3.1

Solving Equations Introduction

ACT OPENER1. What is 25% of 80

miles? A. 0.8 milesB. 24 milesC. 80 milesD. 20 milesE. 8 miles

2. Convert 9/25 to a percentage. A. 0.36%B. 3.6%C. 36%D. 9%E. 25%

3. A football team played 27 games and won ¾ of the games. How many games did they lose?

4. If 2.5 pounds of apples cost $2.35 at Kroger and 3 pounds of apple cost $2.70 at Wal-Mart, which store offers the best deal per pound?

A little background information: Two soccer teams are tied at half time: 2 to

22 = 2

If each team scores 3 goals in the next half, the score will now be tied. 2 + 3 = 2 + 3

Addition Property of EqualityIf the same number is added to equal

numbers, the sums are equal.

A little more background info….Two sporting goods store charge $36 for a

soccer ball. 36 = 36

If during a spring sale, each store reduces the price by $5, both stores will be charging the same price. 36 -5 = 36 -5

If the same number is subtracted from equal numbers, the differences are equal.

The same holds true for multiplication and division.

The Keys to Solving EquationsUse the Properties of Equality

“Whatever you do to one side of the equal sign, do the same thing to the opposite side of the equal sign.”

Ex: If you multiply by -1 on the left side, then you must multiply by -1 on the right side.

Use the opposite operation to solve equations. The opposite of addition is _______________. The opposite of subtraction is _______________. The opposite of multiplication is _______________. The opposite of division is _________________.

MOST IMPORTANTLY, SHOW ALL OF YOUR WORK!

subtraction

addition

multiplication

division

Practice with One-Step1. x + 8 =19

2. x – 3 =5

3. 3x = 12

4. 52

x

Practice with Two-Step5.) 2x – 7 = 13

6.)

7.) 5x + 4 = 29

8.) 933

x

232

x

Practice with Distributive PropertyWe use the distributive property to

eliminate the parentheses (or groupings).

9.) 2(2x + 6) = 20 10.) 6(x-3) = 24

Practice combining like terms11.) 2x + 6x = 30 12.) 7x + 8 – 3x = 32

Solving Equations Relay

Exit Slip

Homework

Worksheet: Solving Basic Equations (page 21)