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# Solving equations

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### Solving equations

1. 1. Section 3.1 Solving Equations Introduction
2. 2. ACT OPENER <ul><li>What is 25% of 80 miles? </li></ul><ul><ul><ul><li>0.8 miles </li></ul></ul></ul><ul><ul><ul><li>24 miles </li></ul></ul></ul><ul><ul><ul><li>80 miles </li></ul></ul></ul><ul><ul><ul><li>20 miles </li></ul></ul></ul><ul><ul><ul><li>8 miles </li></ul></ul></ul><ul><li>Convert 9/25 to a percentage. </li></ul><ul><ul><ul><li>0.36% </li></ul></ul></ul><ul><ul><ul><li>3.6% </li></ul></ul></ul><ul><ul><ul><li>36% </li></ul></ul></ul><ul><ul><ul><li>9% </li></ul></ul></ul><ul><ul><ul><li>25% </li></ul></ul></ul><ul><li>A football team played 27 games and won ¾ of the games. How many games did they lose? </li></ul><ul><li>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? </li></ul>
3. 3. A little background information: <ul><li>Two soccer teams are tied at half time: 2 to 2 </li></ul><ul><ul><li>2 = 2 </li></ul></ul><ul><li>If each team scores 3 goals in the next half, the score will now be tied. </li></ul><ul><ul><li>2 + 3 = 2 + 3 </li></ul></ul><ul><li>Addition Property of Equality </li></ul><ul><ul><li>If the same number is added to equal numbers, the sums are equal. </li></ul></ul>
4. 4. A little more background info…. <ul><li>Two sporting goods store charge \$36 for a soccer ball. </li></ul><ul><ul><li>36 = 36 </li></ul></ul><ul><li>If during a spring sale, each store reduces the price by \$5, both stores will be charging the same price. </li></ul><ul><ul><li>36 -5 = 36 -5 </li></ul></ul><ul><li>If the same number is subtracted from equal numbers, the differences are equal. </li></ul><ul><li>The same holds true for multiplication and division. </li></ul>
5. 5. The Keys to Solving Equations <ul><li>Use the Properties of Equality </li></ul><ul><ul><li>“ Whatever you do to one side of the equal sign, do the same thing to the opposite side of the equal sign.” </li></ul></ul><ul><ul><li>Ex: If you multiply by -1 on the left side, then you must multiply by -1 on the right side. </li></ul></ul><ul><li>Use the opposite operation to solve equations. </li></ul><ul><ul><li>The opposite of addition is _______________. </li></ul></ul><ul><ul><li>The opposite of subtraction is _______________. </li></ul></ul><ul><ul><li>The opposite of multiplication is _______________. </li></ul></ul><ul><ul><li>The opposite of division is _________________. </li></ul></ul><ul><li>MOST IMPORTANTLY, SHOW ALL OF YOUR WORK! </li></ul>subtraction addition multiplication division
6. 6. Practice with One-Step <ul><li>x + 8 =19 </li></ul><ul><li>x – 3 =5 </li></ul><ul><li>3x = 12 </li></ul>
7. 7. Practice with Two-Step <ul><li>5.) 2x – 7 = 13 </li></ul><ul><li>6.) </li></ul>7.) 5x + 4 = 29 8.)
8. 8. Practice with Distributive Property <ul><li>We use the distributive property to eliminate the parentheses (or groupings). </li></ul><ul><li>9.) 2(2x + 6) = 20 10.) 6(x-3) = 24 </li></ul>
9. 9. Practice combining like terms <ul><li>11.) 2x + 6x = 30 12.) 7x + 8 – 3x = 32 </li></ul>
10. 10. Solving Equations Relay
11. 11. Exit Slip
12. 12. Homework <ul><li>Worksheet: Solving Basic Equations (page 21) </li></ul>