Mathematics for science and technology
Mathematics for science and technology

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Mathematics for science and technology

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.

multiline equation row 1 four times x equals 24 row 2 four times x divided by four equals 24 divided by four

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

Timing: Allow about 5 minutes

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

Answer

  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

Timing: Allow about 15 minutes

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
  8. four times x divided by five equals 12
  9. equation left hand side x divided by three equals right hand side two divided by five
  10. m divided by three plus m divided by five equals two
  11. x divided by four minus x divided by seven equals two

Answer

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.four times x divided by five equals 124x = 60x = 15
i.equation left hand side x divided by three equals right hand side two divided by fivex equals six divided by fivex = 1.2
j.m divided by three plus m divided by five equals twom plus three times m divided by five equals six5m + 3m = 30m = 3.75
k.x divided by four minus x divided by seven equals twox minus four times x divided by seven equals eight7x – 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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