01 Linear Equations in One Variable.pptx
- 1. Linear Equations in One Variable G7 MATHEMATICS
- 2. LESS ON SOLVING EQUATIONS USING ADDITION AND SUBTRACTION 01 In algebra there are operations that “undo” each other such as addition and subtraction. For example, if you start with 8 and add 6, you can get back to 8 by subtracting 6 as shown below.
- 3. LESS ON 01 SOLVING EQUATIONS USING ADDITION AND SUBTRACTION
- 4. Solve the equation:x + 5 = 11 Solution: Your goal is to isolate the variable x. x + 5 = 11 Write the original equation. x + 5 - 5 = 11 - 5 Subtract 5 from both sides to isolate the variable on the left hand side. x = 6 Check: Substitute 6 for the variable in the original equation. x + 5 = 11 6 + 5 = 11 11 = 11 Write the original equation. Substitute 6 for x. Both sides are equal therefore our answer is correct.
- 5. Solve the equation:15 = a + 8 Solution: Your goal is to isolate the variable a. 15 = a + 8 Write the original equation. 15 - 8 = a + 8 - 8 Subtract 8 from both sides to isolate the variable on the right hand side. 7 = a Check: Substitute 7 for the variable in the original equation. 15 = a + 8 15 = 7 + 8 15 = 15 Write the original equation. Substitute 7 for a. Both sides are equal therefore our answer is correct.
- 6. Solve the equation: y - 7 = 10 Solution: Your goal is to isolate the variable y. y - 7 = 10 Write the original equation. y - 7 + 7 = 10 + 7 Add 7 from both sides to isolate the variable on the left hand side. y = 17 Check: Substitute 17 for the variable in the original equation. y - 7 = 10 17 - 7 = 10 10= 10 Write the original equation. Substitute 17 for y. Both sides are equal therefore our answer is correct.
- 7. Solve the equation: n - 15 = - 4 Solution: Your goal is to isolate the variable n. n - 15 = - 4 Write the original equation. n - 15 + 15 = - 4 + 15 Add 15 from both sides to isolate the variable on the left hand side. n = 11 Check: Substitute 11 for the variable in the original equation. n - 15 = - 4 11 - 15 = - 4 -4= - 4 Write the original equation. Substitute 11 for n. Both sides are equal therefore our answer is correct.
- 8. Solve the equation: 7x - 3 = 6x - 7 Solution: Your goal is to isolate the variable x. 7x - 3 = 6x - 7 Write the original equation. 7x - 6x = - 7 + 3 Transpose 6x on the left hand side and the constant -3 on the right hand side. Combine like terms. x = -4 Check: 7x - 3 = 6x - 7 7(-4) - 3 = 6(-4) -7 -28 - 3 = -24 - 7 Write the original equation. Substitute -4 for x. -31 = -31 Simplify.
- 10. LESS ON Solve each equation. Show your solution. 01 1)10 + x = 19 2)-7 + x = -5 3)5x + 7 = 4x +15 4)3f - 12 = 2f + 3 Please see the Jamboard file attached along with this presentation for the solutions.
- 11. LESS ON SOLVING EQUATIONS USING MULTIPLICATION AND DIVISION 01 Like addition and subtraction, multiplication and division are inverse operations. For example, if you start with 3 and multiply it by 8, you can get back to 3 by dividing 24 by 8 as shown below.
- 12. LESS ON 01 SOLVING EQUATIONS USING MULTIPLICATION AND DIVISION
- 13. Solve the equation: 8x = 72 Solution: Your goal is to isolate the variable x. 8x = 72 Write the original equation. 8x = 72 Divide both sides by 8 to get rid of the numerical coefficient 8 beside x. x = 9 8 8 Check: Substitute 9 for the variable in the original equation. 8x = 72 8(9) = 72 72 = 72 Thus, the solution is 9.
- 14. Solve the equation: 85 = 5x Solution: Your goal is to isolate the variable x. 85 = 5x Write the original equation. 85 = 5x Divide both sides by 5 to get rid of the numerical coefficient 5 beside x. 17 = x 5 5 Check: Substitute 17 for the variable in the original equation. 85 = 5x 85 = 5(17) 85= 85 Thus, the solution is 17.
- 15. Solve the equation: x Solution: Your goal is to isolate the variable x. Write the original equation. Multiply both sides by 6 to get rid of the 6 in the denominator on the left hand side. x = 48 Check: Substitute 48 for the variable in the original equation. Thus, the solution is 48. 6 = 8 x 6 = 8 x 6 = 8 (6) (6) x 6 = 8 48 6 = 8 8 = 8
- 16. -32 = -32 = -32 Solve the equation: n Solution: Your goal is to isolate the variable n. Write the original equation. Multiply both sides by 8 to get rid of the 8 in the denominator on the left hand side. n = -256 Check: Substitute -256 for the variable in the original equation. Thus, the solution is -256. 8 = -32 n 8 = -32 n 8 = -32 (8) (8) n 8 = -32 -256 8
- 17. LET’S PRACTICE!
- 18. LESS ON 01 1)-9y = 81 2)15d = 40 3)25f = -25 4)b = 9 Solve each equation. Show your solution. 3 5) 15 = c
- 20. LESS ON Now you have been able to solve every equation by applying a single inverse operation. Such an equation is called one-step equation. Some equations involve two operations. To solve these two-step equations, undo addition and subtraction first. Then, undo multiplication and division.
- 21. Example: 2x + 6 = 14 2x + 6 = 14 2x = 14 - 6 2x = 8 2x = 8 2 2 x = 4 transpose + 6
- 22. Example: 10x - 4 - 5x=16 10x - 4 - 5x =16 10x - 5x =16+4 5x = 20 5x = 20 5 5 x = 4 transpose - 4
- 23. Example: transpose x + 9 = -5 4 x + 9 = -5 4 + 9 x = -5 - 9 4 x = -14 4 x = -14 4 (4) (4) x = -56
- 24. Example: transpose n - 8 = 10 3 n - 8 = 10 3 n = 10 + 8 3 n = 18 3 n = 18 3 (3) (3) n = 54
- 25. LESS ON 01 1)-18 + 4y = 10 2)5x - 13 = 3 + 3x 3)m + 5 = 11 Solve each equation. Show your solution. 2
- 26. Worksheet #1
- 27. LESS ON Worksheet #1A Solve each equation. Show your solution. 01 1) x -7 = 9 2) 3 + x = -4 3) -35 + x =7 4) 7x-4 = 6x +28 5) 6x + 2 = 5x + 18
- 28. LESS ON Worksheet #1B Solve each equation. Show your solution. 01 1) 7x = 42 2) -6t = 12 3) -n = 33 4) x = 2 13 5) a = 12 -3
- 29. LESS ON Worksheet #1C Solve each equation. Show your solution. 01 1) 3x - 4 = 11 2) 2a + 5 = 13 3) 4d - 5 = 2d + 9 4) 9e + 3 = 7e - 11 5) c - 6 = 4 5
- 30. LESS ON PRACTICE: 01 Use the words multiply or divide to complete each statement. 1. To solve , ___________ both sides of the equation by 15. _b_ 15 = -12 2. To solve , ___________ both sides of the equation by 10. 10c = 130
- 31. LESS ON _b_ 15 = -12 _b_ 15 = -12 (15) (15) b = 180 10c = 130 10 10 c = 13 10c = 130 PRACTICE: