One step equations

1. One step equations

2. ONE STEP EQUATIONS An equation is like a balance scale because it shows that two quantities are equal. What you do to one side of the equation must also be done to the other side to keep it balanced.

3. One way to solve an equation is to use inverse operations. • An inverse operation is an operation that “undoes” • another operation. • Addition and subtraction are inverse operations. • Multiplication and Division are inverse operations. • *Performing the same operation on each side of an • equation results in a new equation that has the same solution as the original equation. • Today we will focus on adding and subtracting operations

4. x + 8 = 15 1) Solve x + 8 = 15 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

5. 1) Solve x + 8 = 15 To solve, you must get the variable by itself. What number is on the same side as x? 8 To get x by itself, we must undo the “add 8”. What is the opposite of addition? Subtract 8

6. 1) Solve x + 8 = 15 - 8 -8 x = 7 7 + 8 = 15 • Draw “the river” to separate the equation into 2 sides • Subtract 8 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

7. r + 16 = -7 1) Solve r + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

8. 1) Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

9. 1) Solve r + 16 = -7 - 16 -16 r = -23 -23 + 16 = -7 • Draw “the river” to separate the equation into 2 sides • Subtract 16 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

10. Answer Now 2) Solve x + 2 = -3Get the variable by itself. What is your first step? • Add 2 to both sides • Subtract 2 from both sides • Add 3 to both sides • Subtract 3 from both sides

11. 2) Solve x + 2 = -3 - 2 - 2 x = -5 -5 + 2 = -3 • Draw “the river” to separate the equation into 2 sides • Subtract 2 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem On practice and assessments, be sure to check your work!! There is no reason why you should miss a problem!

12. 3) Solve 8 = m - 3 + 3 + 3 11= m 8 = 11 - 3 • Draw “the river” to separate the equation into 2 sides • Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

13. Answer Now 3) Solve 8 = m - 5 • m = 3 • m = 11 • m = 13 • m = 8/3

14. When solving equations, we want to eliminate double signs. y + (-3) = 8 is rewritten as y – 3 = 8 p – (-5) = 6 is rewritten as p + 5 = 6 As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”. This will make things less confusing in the future!

15. 4) Solve y + (-3) = 7 y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 • Draw “the river” to separate the equation into 2 sides • Eliminate the double sign • Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

16. Draw “the river” to separate the equation into 2 sides • Eliminate the double sign • Subtract 2 from both sides • Simplify vertically • 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? • Check your answer x + 2 = 1 - 2 - 2 x = -1 -1 + 2 = 1 5) Solve. x - (-2) = 1