By LearningExpress Editors

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.

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

From Basic Math in 15 Minutes A Day. Copyright © 2008 by LearningExpress, LLC. All Rights Reserved.

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