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1. 1. Objective The student will be able to: solve equations using addition and subtraction. Designed by Skip Tyler, Varina High School
2. 2. <ul><li>To solve an equation means to isolate the variable on one side of the equation. </li></ul><ul><li>You can do this by using the addition/subtraction property of equality. </li></ul>
3. 3. 1) Solve r + 16 = -7 <ul><li>Think of this equation as a balance scale. </li></ul>Whatever you do to one side has to be done to the other to keep it balanced! r + 16 -7 =
4. 4. 1) Solve r + 16 = -7 <ul><li>To solve, you must get the variable by itself. </li></ul><ul><li>What number is on the same side as r? </li></ul><ul><li>16 </li></ul><ul><li>To get r by itself, we must undo the “add 16”. What is the opposite of addition? </li></ul><ul><li>Subtract 16 </li></ul>
5. 5. 1) Solve r + 16 = -7 <ul><li>Draw “the river” to separate the equation into 2 sides </li></ul><ul><li>Subtract 16 from both sides </li></ul><ul><li>Simplify vertically </li></ul><ul><li>Check your answer by substituting your answer back into the problem </li></ul>- 16 -16 r = -23 -23 + 16 = -7
6. 6. 2) Solve x + 2 = -3 Get the variable by itself. What is your first step? <ul><li>Add 2 to both sides </li></ul><ul><li>Subtract 2 from both sides </li></ul><ul><li>Add 3 to both sides </li></ul><ul><li>Subtract 3 from both sides </li></ul>Answer Now
7. 7. 2) Solve x + 2 = -3 <ul><li>Draw “the river” to separate the equation into 2 sides </li></ul><ul><li>Subtract 2 from both sides </li></ul><ul><li>Simplify vertically </li></ul><ul><li>Check your answer by substituting your answer back into the problem </li></ul>- 2 - 2 x = -5 -5 + 2 = -3 On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!
8. 8. 3) Solve 8 = m - 3 <ul><li>m = 5 </li></ul><ul><li>m = 11 </li></ul><ul><li>m = 24 </li></ul><ul><li>m = 8/3 </li></ul>Answer Now
9. 9. 3) Solve 8 = m - 3 + 3 + 3 11= m 8 = 11 - 3 <ul><li>Draw “the river” to separate the equation into 2 sides </li></ul><ul><li>Add 3 to both sides </li></ul><ul><li>Simplify vertically </li></ul><ul><li>Check your answer by substituting your answer back into the problem </li></ul>
10. 10. When solving equations, we want to eliminate double signs. <ul><li>y + ( - 3) = 8 </li></ul><ul><li>is rewritten as </li></ul><ul><li>y – 3 = 8 </li></ul><ul><li>p – ( - 5) = 6 </li></ul><ul><li>is rewritten as </li></ul><ul><li>p + 5 = 6 </li></ul>As a general rule, replace “+ (- )” with “–” and “– (- )” with “+” . This will make things less confusing in the future!
11. 11. 4) Solve y + (-3) = 7 y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 <ul><li>Draw “the river” to separate the equation into 2 sides </li></ul><ul><li>Eliminate the double sign </li></ul><ul><li>Add 3 to both sides </li></ul><ul><li>Simplify vertically </li></ul><ul><li>Check your answer by substituting your answer back into the problem </li></ul>
12. 12. 5) Solve. - x - (-2) = 1 -x + 2 = 1 - 2 - 2 - x = -1 x = 1 -( 1 ) + 2 = 1 <ul><li>Draw “the river” to separate the equation into 2 sides </li></ul><ul><li>Eliminate the double sign </li></ul><ul><li>Subtract 2 from both sides </li></ul><ul><li>Simplify vertically </li></ul><ul><li>We haven’t gotten x by itself. If we read this aloud, it is “the opposite of x equals -1”. What would x be equal? </li></ul><ul><li>Check your answer </li></ul>
13. 13. Solve -y – (-3) = 7 <ul><li>y = 10 </li></ul><ul><li>y = 4 </li></ul><ul><li>y = -10 </li></ul><ul><li>y = -4 </li></ul>Answer Now
14. 14. Journal <ul><li>What do you think Algebra is? </li></ul><ul><li>Give an example and explain why you feel this way. </li></ul>