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Solve for \( x \) Exercises with Verification Steps

This document provides a series of exercises focused on solving linear equations for ( x ) and verifying results through substitution. The exercises cover a variety of equations, such as ( 4x + 7 = 35 ), ( 9x + 2 = 3x + 38 ), and others, requiring the application of algebraic manipulation and checking of solutions by substituting the values back into the original equations. Each example guides the reader through the solving process and emphasizes the importance of verification in achieving accurate results.

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Solve for \( x \) Exercises with Verification Steps

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  1. Chapter 10 Section 10.6 Exercise #5

  2. Solve for x and check your result. 4x + 7 = 35 4x + 7 + (– 7) = 35 + (– 7) 4x 28 = 4 4 x = 7 Check your answer.

  3. Solve for x and check your result. 4x + 7 = 35 4(7) + 7 = 35 28 + 7 35 =  = 35 35 x = 7 Check your answer.

  4. Chapter 10 Section 10.6 Exercise #15

  5. 1 1 Solve for x and check your result. + (– 5) = 3 + (– 5) + 5 = 3 + 5 4 (4) 8 = x = 32 Check your answer.

  6. 8 1 Solve for x and check your result. + (– 5) = 3 + (– 5) = 3  3 = 3 x = 32 Check your answer.

  7. Chapter 10 Section 10.6 Exercise #19

  8. 1 4 1 1 1 1 Solve for x and check your result. + (– 3) = 13 + (– 3) + 3 = 13 + 3 16 = x = 20 Check your answer.

  9. (20) 4 1 x = 20 Solve for x and check your result. + (– 3) = 13 + (– 3) = 13 16 + (– 3) = 13  13 = 13 Check your answer.

  10. Chapter 10 Section 10.6 Exercise #25

  11. 6 1 1 1 Solve for x and check your result. 9x + 2 = 3x + 38 9x + 2 + (– 2) = 3x + 38 + (– 2) 9x = 3x + 36 9x + (– 3x) = 3x + (– 3x) + 36 6x = 36 6 6 x = 6 Check your answer.

  12. Solve for x and check your result. 9x + 2 = 3x + 38 9(6) + 2 = 3(6) + 38 + 54 2 = 18 + 38  56 = 56 x = 6 Check your answer.

  13. Chapter 10 Section 10.2 Exercise #37

  14. Solve for x and check your result. 6x + 7 + (– 4x) = 8 + 7x + (– 26) 2x + 7 = 7x + (– 18) 2x + 7 + 18 = 7x + (– 18) + 18 2x + 25 = 7x + 2x + (– 2x) 25 = 7x + (– 2x) 25 = 5x 5 5 5 = x Check your answer.

  15. Solve for x and check your result. 6x + 7 + (– 4x) = 8 + 7x + (– 26) + (– 4(5)) (– 26) 6(5) + 7 = 8 + 7(5) + (– 20) + (– 26) 30 + 7 + = 8 + 35  17 = 17 5 = x Check your answer.

  16. Chapter 10 Section 10.6 Exercise #45

  17. Solve for x and check your result. 3x + 2(4x + (– 3)) = 6x + (– 9) 3x + 8x = 6x + (– 9) (– 6) + 11x + 6x (– 6) = + (– 9) 11x + (– 6) + 6 = 6x + (– 9) + 6 (– 3) 11x = 6x + 11x + (– 6x) = 6x + (– 6x) + (– 3) 5x = – 3 5 5 Check your answer. x =

  18. 2 2 Check your answer. x = Solve for x and check your result. 3x + 2(4x + (– 3)) = 6x + (– 9) 3 + 4 + (–3) = 6 + (–9) + + (–3) = + (–9)

  19. 3 + 2 4 + (–3) = 6 + (–9) + + = + 2 Check your answer. x = Solve for x and check your result. 3x + 2(4x + (– 3)) = 6x + (– 9) (–3) (–9) 2 = +

  20. 3 + 2 4 + (–3) = 6 + (–9) + + = + 2 = + Check your answer. x = Solve for x and check your result. 3x + 2(4x + (– 3)) = 6x + (– 9)

  21. 3 + 2 4 + (–3) = 6 + (–9) + + = + 2 = Check your answer. x = Solve for x and check your result. 3x + 2(4x + (– 3)) = 6x + (– 9) 

  22. Chapter 10 Section 10.6 cut!!!!!!!!!!!!!!!!!!!! Exercise #49

  23. Chapter 10 Section 10.6 Exercise #53

  24. There were 55 more yes votes than no votes on an election measure. If 735 votes were cast in all, how many yes votes were there? The number of yes votes = x. The number of no votes =x – 55. Total votes =735.

  25. The number of yes votes = x. The number of no votes =x – 55. Total votes =735. (x – 55) + x = 735

  26. The number of yes votes = x. The number of no votes =x – 55. Total votes =735. x (– 55) + x = 735 + 2x (– 55) + = 735 2x + (– 55) 55 55 + = 735 + 2x = 790 2 2

  27. x (– 55) + x = 735 + 2x (– 55) + = 735 2x + (– 55) 55 55 + = 735 + The number of yes votes = x. The number of no votes =x – 55. Total votes =735. x = 395 Check your answer.

  28. (x – 55) + x = 735 The number of yes votes = x. The number of no votes =x – 55. Total votes =735. ( – 55) + 395 = 735 395 (340) + 395 = 735  735 = 735 x = 395 Check your answer. There were 395 yes votes.

  29. Chapter 10 Section 10.6 cut!!!!!!!!!!!!!!!! Exercise #55

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