Chapter 3.2 and 3.3 – Solving One-Step Equations

1. Chapter 3.2 and 3.3 – Solving One-Step Equations

2. An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. A solution set is the set of all solutions. Finding the solutions of an equation is also called solving the equation.

3. Add x. Subtract x. Multiply by x. Divide by x. To find solutions, perform inverse operations until you have isolated the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side. Inverse Operations An equation is like a balanced scale. To keep the balance, you must perform the same inverse operation on both sides of the equation.

5. y – 8 = 24 Check Example 1 - Solve the equation and then check your solution. y – 8 = 24 Since 8 is subtracted from y, add 8 to both sides to undo the subtraction. + 8+ 8 y = 32 To check your solution, substitute 32 for y in the original equation. 32 – 824  2424

6. 4.2 = t + 1.8 Check Example 2 - Solve the equation and then check your solution. 4.2 = t + 1.8 Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition. –1.8–1.8 2.4 = t To check your solution, substitute 2.4 for t in the original equation. 4.2 2.4 + 1.8  4.2 4.2

7. –6 = k– 6 Check Example 3 - Solve the equation. Check your answer. –6 = k –6 + 6+ 6 Since 6 is subtracted from k, add 6 to both sides to undo the subtraction. 0= k To check your solution, substitute 0 for k in the original equation. –6 0– 6 –6 –6 

9. –24 = –6v Check Example 4 - Solve the equation. Check your answer. –24 = –6v Since v is multiplied by –6, divide both sides by –6 to undo the multiplication. -6 -6 4= v To check your solution, substitute 4 for v in the original equation. –24 –6(4)  –24 –24

10. Check Example 5 - Solve the equation. Check your answer. Since j is divided by 3, multiply from both sides by 3 to undo the division. –24 = j To check your solution, substitute –24 for j in the original equation.  –8 –8

11. y = –20 0.5y =–10 Check Example 6 - Solve each equation. Check your answer. 0.5y = –10 Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication. To check your solution, substitute –20 for y in the original equation. 0.5(–20) –10 –10 –10 

12. The reciprocal of is . Since w is multiplied by multiply both sides by . Example 7 - Solve each equation. Then check your solution. Check : , , -20 = -20

13. The reciprocal of is . Since w is multiplied by multiply both sides by . Check Example 8 - Solve the equation. Check your answer. w = 612 To check your solution, substitute 612 for w in the original equation. 102 102 

14. Ciro deposits of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find out how much money Ciro earned mowing lawns this year. 1 4 Additional Example 9: Application

15. times earnings is $285 1 e = $285 4 The reciprocal of is . Since e is multiplied by , multiply both sides by 4 1 1 4 4 1 4 1 4 1 4 1 . 4  e = 285  1 Additional Example 9 Continued Write an equation to represent the relationship. e = $1140 The original earnings were $1140 .

16. Tricky Problems Solve and check each equation a.) f + (-14) = 10 b.) y – (– 1.3) = 2.4 c.) x = 24 y = 1.1 a = 5

17. Chapter 3.2 and 3.3 Review…Solve and check each equation1.) (– 3) + x = 10 2.) y – (–2.4) = 8.53.) – 7a = 56 4.) x = 13 y = 6.1 a = -8 x = -12