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Either paper 1 mark
\(9x = 54\)
Work out the value of \(x\).
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\(6\)Both sides divide by 9:
\(x = \frac{ 54 }{ 9 } = 6\)
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Either paper 1 mark
\(x - 6 = -14\)
Work out the value of \(x\).
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\(-8\)Add 6 to both sides:
\(x = -14 - (-6) = -8\)
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Either paper 1 mark
Solve the equation \(\frac{x}{ 10 } = 5\)
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\(50\)\(x\) has been divided by 10, so multiply both sides by 10:
\(x = 5 \times 10 = 50\)
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Either paper 2 marks
Solve the equation \(-8x = 56\)
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\(-7\)Divide both sides by \(-8\):
\(x = \frac{ 56 }{ -8 } = -7\)
Check: \(-8 \times -7 = 56\)
- M1divides both sides by \(-8\)
- A1\(x = -7\)
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Either paper 2 marks
Solve the equation \(28 - x = 14\)
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\(14\)Add \(x\) to both sides so that the \(x\) term is positive:
\(28 = 14 + x\)
Subtract 14 from both sides:
\(x = 28 - (14) = 14\)
- M1adds \(x\) to both sides: \(28 = 14 + x\)
- A1\(x = 14\)
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Either paper 2 marks
Solve \(x + 0.6 = 15.4\)
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\(14.8\)Subtract 0.6 from both sides:
\(x = 15.4 - 0.6 = 14.8\)
- M1subtracts 0.6 from both sides: \(x = 15.4 - 0.6\)
- A1\(x = 14.8\)
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Either paper 3 marks
A shop sells paint brushes. Each paint brush costs \(c\) pounds.
(a)Naomi buys 3 paint brushes. She pays £39 altogether.
Write down an equation in terms of \(c\).
(b)Solve your equation to find the cost of one paint brush.
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(a) \(3c = 39\)
(b) \(\text{£}13\)3 paint brushes at \(c\) pounds each cost \(3c\) pounds, and that came to £39:
\(3c = 39\)
Divide both sides by 3:
\(c = \frac{ 39 }{ 3 } = 13\)
One paint brush costs £13.
- (b) M1divides both sides by 3: \(c = \frac{ 39 }{ 3 }\)
- (b) A1cost of one paint brush £13
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Either paper 2 marks
The solution of the equation
\(\frac{x}{ a } = 3\)
is \(x = 27\).
Calculate the value of \(a\).
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\(9\)Substitute \(x = 27\).
\(\frac{ 27 }{ a } = 3\)
Dividing 27 by \(a\) gives 3, so \(a\) is 27 divided by 3.
\(a = 27 \div 3 = 9\)
- M1substitutes \(x = 27\) to get \(\frac{ 27 }{ a } = 3\), or 27 \(\div\) 3
- A1\(a = 9\)
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Either paper 1 mark
\(6x = 66\)
Work out the value of \(x\).
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\(11\)Both sides divide by 6:
\(x = \frac{ 66 }{ 6 } = 11\)
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Either paper 1 mark
Solve \(x - 6 = 2\)
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\(8\)Add 6 to both sides:
\(x = 2 - (-6) = 8\)