# 4 Solving simple equations with one unknown

Consider the equation 4*x* = 24. As it is written *x* is the unknown and to solve this equation you need to find the value of *x* which makes the statement 4*x* = 24 true.

You may be able to see this straight away, but if not, divide both sides of the equation by 4, to get an answer for *x*.

The solution is, therefore, *x* = 6.

You can check the accuracy of your answer by substituting the value for x back into the original equation: 4 × 6 = 24.

Try this examples for yourself now.

## Activity 4 Solving equations

Now solve the following equations for *x*.

- 3
*x*= 6 - 7
*x*= 21 - 8
*x*= 32 *x*+ 3 = 9*x*+ 6 = 7*x*+ 7 = 11

### Answer

- 3
*x*= 6 divide both sides by 3:*x*= 2 - 7
*x*= 21 divide both sides by 7:*x*= 3 - 8
*x*= 32 divide both sides by 8:*x*= 4 *x*+ 3 = 9 subtract 3 from both sides :*x*= 6*x*+ 6 = 7 subtract 6 from both sides :*x*= 1*x*+ 7 = 11 subtract 7 from both sides :*x*= 4

Now you’ve warmed up try some slightly more complex equations, which involve rearranging equations and multiplying out of brackets.

## Activity 5 More complex equations

Now solve the following equations for *m*.

- 2
*x*– 1 = 7 - 5
*x*– 8 = 2 - 3
*x*+ 8 = 5 - 3
*x*– 8 = 5*x*– 20 - 3(
*x*+ 1) = 9 - 23 –
*x*=*x*+ 11 - 2(
*x*– 3) – (*x*– 2) = 5

### Answer

Equation | Step 1 | Step 2 | Solution | |
---|---|---|---|---|

a. | 2x – 1 = 7 | 2x – 8 | x = 4 | |

b. | 5x – 8 = 2 | 5x = 10 | x = 2 | |

c. | 3x + 8 = 5 | 3x = –3 | x = –1 | |

d. | 3x – 8 = 5x – 20 | –8 = 5x – 3x – 20 | 12 = 2x | x = 6 |

e. | 3(x + 1) = 9 | 3x + 3 = 9 | 3x = 6 | x = 2 |

f. | 23 – x = x + 11 | 23 = 2x + 11 | 2x = 12 | x = 6 |

g. | 2(x – 3) – (x – 2) = 5 | 2x – 6 – x + 2 = 5 | x – 4 = 5 | x = 9 |

h. | 4x = 60 | x = 15 | ||

i. | x = 1.2 | |||

j. | 5m + 3m = 30 | m = 3.75 | ||

k. | 7x – 4x = 56 | x = 18.7 (to 1 decimal place) |

Rather than solving just one equation in the next section you will learn about pairs of equations with two unknowns.