2. Algebra Solving Linear Equations 3 x = 6 x = 2 Change side,change sign

4. The scales are perfectly balanced Removing the same weights from BOTH sides will keep the scales balanced Picture a set of weighing scales Solve 5x + 1 = 2x + 7 1 xx xxx xx 111 11 1 1 CHECK substitute x = 2 into 5x + 1 = 2x + 7 5x + 1 = 5  2 + 1 = 10 + 1 = 11 2x + 7 = 2  2 + 7 = 4 + 7 = 11 This leaves us with: 3x = 6 We can see that: x = 2

5. Solve 3 x + 10 = 5x + 2 x xx Picture a set of weighing scales The scales are perfectly balanced Removing the same weights from BOTH sides will keep the scales balanced This leaves us with: 11 1 x x x x 11 1 1 1 x 1 11 1 8 = 2x We can see that: x = 4 CHECK substitute x = 4 into 3x + 10 = 5x + 2 3x + 10 = 3  4 + 10 = 12 + 10 = 22 5x + 2 = 5  4 + 2 = 20 + 2 = 22

7. - + 7 Solve the equation 5x + 1 = 2x + 7 5x5x Take 2x to the other side of the equation and change the sign ( + to - ) + 1 2x2x = Take +1 to the other side of the equation and change the sign ( + to - ) 3x3x 7 = 3 6 = Take 3 to the other side of the equation and change the sign ( x to ÷ ) x 2 = x 1

8. + 2 5x5x 3x3x - Solve the equation 3x + 10 = 5x + 2 Take 3x to the other side of the equation and change the sign ( + to - ) + 10 = Take +2 to the other side of the equation and change the sign ( + to - ) 8 x = Take 2 to the other side of the equation and change the sign ( x to ÷ ) x = 4 + 2 2x2x 10 = 2 2

9. 4x + 1 = 3x + 11 4x  7 = 3x + 2 3x + 1 = 2x + 9 3x  1 = 9 - 2x 4x + 2 = 2x - 8 4x  2 = 2x - 5 9x + 4 = 7x + 20 3x  5 = 2x + 7 3x  7 = - x + 9 4x + 10 = x + 40 Solve the following equations. Solution AnswersAnswers

10. 4x + 1 = 3x + 11 4x + 1 = 3x + 11 4x – 3x = 11 - 1 x = 10

11. 4x - 7 = 3x + 2 4x - 7 = 3x + 2 4x – 3x = 2 + 7 x = 9

12. 3x + 1 = 2x + 9 3x + 1 = 2x + 9 3x – 2x = 9 – 1 x = 8

13. 5 x = 10 3x – 1 = 9 – 2x 3x – 1 = 9 – 2x 3x + 2x = 9 + 1 5 x = 10 x = 2

14. x = - 5 4x + 2 = 2x – 8 4x + 2 = 2x – 8 4x – 2x = - 8 – 2 2 x = - 10 2 x = - 10

15. or x = -1 x = - 1.5 4x – 2 = 2x – 5 4x – 2 = 2x – 5 4x – 2x = – 5 + 2 2 x = - 3 2 x = – 3 2 1

16. x = 8 9x + 4 = 7x + 20 9x + 4 = 7x + 20 9x – 7x = 20 – 4 2 x = 16 2 x = 16

17. x = 12 3x – 5 = 2x + 7 3x – 5 = 2x + 7 3x – 2x = 7 + 5

18. x = 4 3x – 7 = -x + 9 3x – 7 = - x + 9 3x + x = 9 + 7 4 x = 16 4 x = 16

19. x = 10 4x + 10 = x + 40 4x + 10 = x + 40 3 x = 30 3 x = 30 4x – x = 40 – 10

20. 4x + 1 = 3x + 11 4x  7 = 3x + 2 3x + 1 = 2x + 9 3x  1 = 9 - 2x 4x + 2 = 2x - 8 4x  2 = 2x - 5 9x + 4 = 7x + 20 3x  5 = 2x + 7 3x  7 = - x + 9 4x + 10 = x + 40 Solve the following equations. x = 10 x = 9 x = 8 x = 2 x = -5 x = -1.5 x = 8 x = 12 x = 4 x = 10 QuestionsQuestions