18

\( \frac{a}{7} - 3 = 1 \)

\( \frac{a}{7} = 4 \implies a = 4 \times 7 \)

\( a = 28 \)

19

\( 18 - 5v = 33 \)

\( -5v = 15 \implies v = \frac{15}{-5} \)

\( v = -3 \)

20

\( 21 - 4d = 5 \)

\( -4d = -16 \implies d = \frac{-16}{-4} \)

\( d = 4 \)

21

\( \frac{x + 5}{3} = 7 \)

\( x + 5 = 21 \implies x = 21 - 5 \)

\( x = 16 \)

22

\( \frac{y - 7}{4} = -4 \)

\( y - 7 = -16 \implies y = -16 + 7 \)

\( y = -9 \)

23

\( \frac{m + 14}{5} = 2 \)

\( m + 14 = 10 \implies m = 10 - 14 \)

\( m = -4 \)

24

\( \frac{p - 5}{-3} = 6 \)

\( p - 5 = -18 \implies p = -18 + 5 \)

\( p = -13 \)

25

\( 59 = 6k + 11 \)

\( 48 = 6k \implies k = \frac{48}{6} \)

\( k = 8 \)

Two-Step Equations Answer Key • Indiana Academic Standard 8.AF.1 Page 1 of 2

Teacher Resource Indiana Standard 8.AF.1

Answer Key • Part 2

Two-Step Equations — Full Solutions (26–50)

Steps shown for inverse operations

26

\( -51 = 4w - 7 \)

\( -44 = 4w \implies w = \frac{-44}{4} \)

\( w = -11 \)

27

\( -13 = \frac{n}{4} - 8 \)

\( -5 = \frac{n}{4} \implies n = -5 \times 4 \)

\( n = -20 \)

28

\( 45 = 15 - 3a \)

\( 30 = -3a \implies a = \frac{30}{-3} \)

\( a = -10 \)

29

\( \frac{3x - 7}{2} = 13 \)

\( 3x - 7 = 26 \implies 3x = 33 \)

\( x = 11 \)

30

\( \frac{6 - x}{5} = 4 \)

\( 6 - x = 20 \implies -x = 14 \)

\( x = -14 \)

31

\( 4x + 9 = 22 \)

\( 4x = 13 \implies x = \frac{13}{4} \)

\( x = \frac{13}{4} \)

32

\( 6y - 5 = 16 \)

\( 6y = 21 \implies y = \frac{21}{6} \)

\( y = \frac{7}{2} \)

33

\( 8m + 11 = -2 \)

\( 8m = -13 \implies m = -\frac{13}{8} \)

\( m = -\frac{13}{8} \)

34

\( 5p - 14 = 8 \)

\( 5p = 22 \implies p = \frac{22}{5} \)

\( p = \frac{22}{5} \)

35

\( \frac{2}{3}w + 5 = 17 \)

\( \frac{2}{3}w = 12 \implies w = 12 \times \frac{3}{2} \)

\( w = 18 \)

36

\( \frac{3}{5}k - 7 = 8 \)

\( \frac{3}{5}k = 15 \implies k = 15 \times \frac{5}{3} \)

\( k = 25 \)

37

\( -\frac{4}{5}n + 6 = -6 \)

\( -\frac{4}{5}n = -12 \implies n = -12 \times (-\frac{5}{4}) \)

\( n = 15 \)

38

\( 3a + 17 = 8 \)

\( 3a = -9 \implies a = \frac{-9}{3} \)

\( a = -3 \)

39

\( 7t - 4 = -18 \)

\( 7t = -14 \implies t = \frac{-14}{7} \)

\( t = -2 \)

40

\( 9v + 13 = 4 \)

\( 9v = -9 \implies v = \frac{-9}{9} \)

\( v = -1 \)

41

\( 10x - 31 = 44 \)

\( 10x = 75 \implies x = \frac{75}{10} \)

\( x = \frac{15}{2} \)

42

\( -7y - 19 = 16 \)

\( -7y = 35 \implies y = \frac{35}{-7} \)

\( y = -5 \)

43

\( \frac{x}{8} + 13 = 11 \)

\( \frac{x}{8} = -2 \implies x = -2 \times 8 \)

\( x = -16 \)

44

\( 15 - 4m = 43 \)

\( -4m = 28 \implies m = \frac{28}{-4} \)

\( m = -7 \)

45

\( 6p + 25 = 10 \)

\( 6p = -15 \implies p = -\frac{15}{6} \)

\( p = -\frac{5}{2} \)

46

\( \frac{w - 11}{7} = -3 \)

\( w - 11 = -21 \implies w = -21 + 11 \)

\( w = -10 \)

47

\( -\frac{5}{6}k - 9 = 1 \)

\( -\frac{5}{6}k = 10 \implies k = 10 \times (-\frac{6}{5}) \)

\( k = -12 \)

48

\( 4n + 27 = 6 \)

\( 4n = -21 \implies n = -\frac{21}{4} \)

\( n = -\frac{21}{4} \)

49

\( \frac{3}{2}a + 14 = 5 \)

\( \frac{3}{2}a = -9 \implies a = -9 \times \frac{2}{3} \)

\( a = -6 \)

50

\( 11t - 15 = 40 \)

\( 11t = 55 \implies t = \frac{55}{11} \)

\( t = 5 \)

Criteria Verification • Indiana Academic Standard 8.AF.1 100% Verified

Total Equations 50 Problems

Integer vs. Fraction 43 Int (86%) / 7 Frac (14%)

Sign Distribution 20 Positive / 30 Negative

Max Match Frequency 4% (Max 2 matches ≤ 10%)

Two-Step Equations Answer Key • Indiana Academic Standard 8.AF.1 Page 2 of 2

Two-Step Equations Problem Bank • Indiana Academic Standard 8.AF.1 Page 1 of 2

Item Bank Indiana Standard 8.AF.1

Equations + Solutions

Equations & Solutions Quick Key (1–50)

Paired Format for Direct Import

1. 3x + 7 = 25 x = 6

2. 5y - 8 = 27 y = 7

3. 4m + 15 = -9 m = -6

4. 2p - 19 = -35 p = -8

5. -6k + 14 = 56 k = -7

6. -3w - 14 = 1 w = -5

7. 8n + 23 = 7 n = -2

8. 7a - 12 = 23 a = 5

9. -4t + 18 = -22 t = 10

10. 9x - 17 = 64 x = 9

11. x/3 + 5 = 9 x = 12

12. y/4 - 7 = 1 y = 32

13. m/2 + 11 = 3 m = -16

14. p/5 - 6 = -9 p = -15

15. -w/3 + 8 = 14 w = -18

16. k/(-4) - 5 = -2 k = -12

17. n/6 + 9 = 5 n = -24

18. a/7 - 3 = 1 a = 28

19. 18 - 5v = 33 v = -3

20. 21 - 4d = 5 d = 4

21. (x + 5)/3 = 7 x = 16

22. (y - 7)/4 = -4 y = -9

23. (m + 14)/5 = 2 m = -4

24. (p - 5)/(-3) = 6 p = -13

25. 59 = 6k + 11 k = 8

26. -51 = 4w - 7 w = -11

27. -13 = n/4 - 8 n = -20

28. 45 = 15 - 3a a = -10

29. (3x - 7)/2 = 13 x = 11

30. (6 - x)/5 = 4 x = -14

31. 4x + 9 = 22 x = 13/4

32. 6y - 5 = 16 y = 7/2

33. 8m + 11 = -2 m = -13/8

34. 5p - 14 = 8 p = 22/5

35. (2/3)w + 5 = 17 w = 18

36. (3/5)k - 7 = 8 k = 25

37. (-4/5)n + 6 = -6 n = 15

38. 3a + 17 = 8 a = -3

39. 7t - 4 = -18 t = -2

40. 9v + 13 = 4 v = -1

41. 10x - 31 = 44 x = 15/2

42. -7y - 19 = 16 y = -5

43. x/8 + 13 = 11 x = -16

44. 15 - 4m = 43 m = -7

45. 6p + 25 = 10 p = -5/2

46. (w - 11)/7 = -3 w = -10

47. (-5/6)k - 9 = 1 k = -12

48. 4n + 27 = 6 n = -21/4

49. (3/2)a + 14 = 5 a = -6

50. 11t - 15 = 40 t = 5

Two-Step Equations Problem Bank • Indiana Academic Standard 8.AF.1 Page 2 of 2