This document provides an introduction to solving equations. It explains the key properties of equality that must be followed when solving equations, such as performing the same operation to both sides of the equal sign. Examples are provided to demonstrate applying these properties to solve one-step, two-step, and multi-step equations. Students are instructed to show their work and given practice problems applying the steps to solve different types of equations.

1. Section 3.1 Solving Equations Introduction

2. ACT OPENER What is 25% of 80 miles? 0.8 miles 24 miles 80 miles 20 miles 8 miles Convert 9/25 to a percentage. 0.36% 3.6% 36% 9% 25% A football team played 27 games and won ¾ of the games. How many games did they lose? 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?

3. A little background information: Two soccer teams are tied at half time: 2 to 2 2 = 2 If each team scores 3 goals in the next half, the score will now be tied. 2 + 3 = 2 + 3 Addition Property of Equality If the same number is added to equal numbers, the sums are equal.

4. 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.

5. The Keys to Solving Equations Use 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

6. Practice with One-Step x + 8 =19 x – 3 =5 3x = 12

7. Practice with Two-Step 5.) 2x – 7 = 13 6.) 7.) 5x + 4 = 29 8.)

8. Practice with Distributive Property We use the distributive property to eliminate the parentheses (or groupings). 9.) 2(2x + 6) = 20 10.) 6(x-3) = 24

9. Practice combining like terms 11.) 2x + 6x = 30 12.) 7x + 8 – 3x = 32

10. Solving Equations Relay

11. Exit Slip

12. Homework Worksheet: Solving Basic Equations (page 21)