 Mathematics for science and technology

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# 4 Solving simple equations with one unknown

Consider the equation 4x = 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 4x = 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.

1. 3x = 6
2. 7x = 21
3. 8x = 32
4. x + 3 = 9
5. x + 6 = 7
6. x + 7 = 11

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

1. 2x – 1 = 7
2. 5x – 8 = 2
3. 3x + 8 = 5
4. 3x – 8 = 5x – 20
5. 3(x + 1) = 9
6. 23 – x = x + 11
7. 2(x – 3) – (x – 2) = 5

EquationStep 1Step 2Solution
a.2x – 1 = 72x – 8x = 4
b.5x – 8 = 25x = 10x = 2
c.3x + 8 = 53x = –3x = –1
d.3x – 8 = 5x – 20–8 = 5x – 3x – 2012 = 2xx = 6
e.3(x + 1) = 93x + 3 = 93x = 6x = 2
f.23 – x = x + 1123 = 2x + 112x = 12x = 6
g.2(x – 3) – (x – 2) = 52x – 6 – x + 2 = 5x – 4 = 5x = 9
h.4x = 60x = 15
i.x = 1.2
j.5m + 3m = 30m = 3.75
k.7x – 4x = 56x = 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.

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