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Solving Basic Math Equations Practice Questions

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Updated on Oct 3, 2011

To review how to solve equations, go to Solving Basic Math Equations Study Guide.

Solving Basic Math Equations Practice Questions

Practice

Solve each algebraic equation for the variable.

  1. x + 10 = 14
  2. a –7 = 12
  3. y + (–2) = 15
  4. r + 3 = 21
  5. s –9 = 3
  6. 2x = 12
  7. –3t = –21
  8. 5q = –45
  9. 3a + 4 = 13
  10. 2p + 2 = 16
  11. 4(c –1) = 12
  12. 3x –4 = 2x + 4
  13. 10w + 14 –8w = 12
  14. 5(b + 1) = 60
  15. 3(y –9) –2 = –35
  16. 4q + 12 = 16
  17. 6(2 + f ) = 5f + 15

Solutions

1. Begin by asking yourself what operation is used in the equation: addition. Then, perform the inverse operation (subtraction) to both sides of the equation:
 
  Finally, combine like terms and solve for the variable.
  x + 0 = 4
  x = 4
2. Begin by asking yourself what operation is used in the equation: subtraction. Then, perform the inverse operation (addition) to both sides of the equation:
 
  Finally, combine like terms and solve for the variable.
  a + 0 = 19
  a = 19
3. Begin by asking yourself what operation is used in the equation: subtraction (addition of a negative number). Then, perform the inverse operation (addition) to both sides of the equation:
 
  Finally, combine like terms and solve for the variable.
  y + 0 = 17
  y = 17
4. Begin by asking yourself what operation is used in the equation: subtraction (addition of a negative number). Then, perform the inverse operation (addition) to both sides of the equation:
 
  Finally, combine like terms and solve for the variable.
  r + 0 = 18
  r = 18
  But you want to solve for r, not –r. So, multiply each side by –1.
  r × –1 = 18 × –1
  r = –18
5. Begin by asking yourself what operation is used in the equation: subtraction. Then, perform the inverse operation (addition) to both sides of the equation:
 
  Finally, combine like terms and solve for the variable.
  s + 0 = 12
  s = 12
6. Begin by asking yourself what operation is used in the equation: multiplication. Then, perform the inverse operation (division) to both sides of the equation:
  2x = 12
 
  Finally, combine like terms and solve for the variable.
  x = 6
7. Begin by asking yourself what operation is used in the equation: multiplication. Then, perform the inverse operation (division) to both sides of the equation:
  –3t = –21
 
  Finally, combine like terms and solve for the variable.
  t = 7
8. Begin by asking yourself what operation is used in the equation: multiplication. Then, perform the inverse operation (division) to both sides of the equation:
  5q = –45
 
  Finally, combine like terms and solve for the variable.
  q = –9
9. Begin by asking yourself what operation is used in the equation: division. Then, perform the inverse operation (multiplication) to both sides of the equation:
  = 3
  4 × = 3 × 4
  Finally, combine like terms and solve for the variable.
  x = 12
10. Begin by asking yourself what operation is used in the equation: division. Then, perform the inverse operation (multiplication) to both sides of the equation:
  = 2
  3 × = 2 × 3
  Finally, combine like terms and solve for the variable.
  x = 6
11. Begin by performing the inverse operation for addition:
 
  3a = 9
  Then, perform the inverse operation for multiplication and solve for a.
 
  a = 3
12. Begin by performing the inverse operation for addition:
 
  Then, perform the inverse operation for multiplication and solve for p.
 
  p = 7
13. First, eliminate the parentheses by multiplying (distributing the 4):
  4(c – 1) = 12
  4c – 4 = 12
  Then, perform the inverse operation for subtraction.
 
  Finally, perform the inverse operation for multiplication and solve for c.
 
  c = 4
14. First, group the variables on one side of the equation by subtracting the smaller of the two variables from both sides:
 
  Then, perform the inverse operation for subtraction and solve for x.
 
15. Begin by grouping like terms together:
  10w + 14 – 8w = 12
  10w – 8w + 14 = 12
  Combine the like terms.
  10w – 8w = 2w
  2w + 14 = 12
  Then, perform the inverse operation for addition.
 
  2w = –2
  Finally, perform the inverse operation for multiplication and solve for w.
 
  w = –1
16. First, eliminate the parentheses by multiplying (distributing the 5).
  5(b + 1) = 60
  5b + 5 = 60
  Then, perform the inverse operation for addition.
 
  5b = 55
  Finally, perform the inverse operation for multiplication and solve for b.
 
  b = 11
17. First, eliminate the parentheses by multiplying (distribute the 3).
  3(y – 9) – 2 = –35  
  3y – 27 – 2 = –35
  Combine the like terms.
  3y – 29 = –35
  Then, perform the inverse operation for subtraction.
 
  Finally, perform the inverse operation for multiplication and solve for y.
 
  y = –2
18. Begin by performing the inverse operation for addition.
 
  Then, perform the inverse operation for multiplication and solve for q.
 
  q = 1
19. Begin by performing the inverse operation for subtraction.
 
  Then, perform the inverse operation for division and solve for t.
  5 × = –6 × 5
  t = –30
20. First, eliminate the parentheses by multiplying (distribute the 6).
  6(2 + f) = 5f + 15
  12 + 6f = 5f + 15
  Then, group the variables on one side of the equation.
 
  Finally, perform the inverse operation for addition and solve for f.
 
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