Higher June 2022 Paper 2 Q5

5 Solve \(\quad 5(2x - 1) = 6x + 9\) [3 marks]

Mark scheme

Answer	Mark	Comments
Alternative method 1
\(10x - 5\)	M1	may be seen in a grid
their \(10x - 6x = 9 +\) their 5 or \(4x = 14\) or \(14 \div 4\) or \(7 \div 2\)	M1	oe eg their \(-5 - 9 = 6x -\) their \(10x\) or \(4x - 14 = 0\) collecting two terms in \(x\) and two constant terms correctly
\(\dfrac{14}{4}\) or \(3\dfrac{2}{4}\) or \(\dfrac{7}{2}\) or \(3\dfrac{1}{2}\) or 3.5	A1ft	oe ft M1M0 or M0M1 with exactly one error
Alternative method 2
\(\dfrac{6x}{5} + \dfrac{9}{5}\)	M1	oe two terms eg \(1.2x + 1.8\)
\(2x -\) their \(\dfrac{6x}{5} =\) their \(\dfrac{9}{5} + 1\) or \(\dfrac{4x}{5} = \dfrac{14}{5}\)	M1	oe eg \(-1 -\) their \(\dfrac{9}{5} =\) their \(\dfrac{6x}{5} - 2x\) or \(\dfrac{4x}{5} - \dfrac{14}{5} = 0\) collecting two terms in \(x\) and two constant terms correctly
\(\dfrac{14}{4}\) or \(3\dfrac{2}{4}\) or \(\dfrac{7}{2}\) or \(3\dfrac{1}{2}\) or 3.5	A1ft	oe ft M1M0 or M0M1 with exactly one error

Ignore simplification or conversion if correct answer seen
Correct answer from trial and improvement	M1M1A1
Correct equation with terms collected or division with no or incorrect answer	M1M1A0
Embedded 3.5 with no or incorrect answer	M1M1A0
\(10x - 5 = 6x + 9\) \(10x - 6x = 9 - 5\) \(x = 1\) (exactly one error in line 2)	M1 M0 A1ft
\(7x - 5 = 6x + 9\) \(7x - 6x = 9 + 5\) \(x = 14\) (exactly one error in line 1)	M0 M1 A1ft
\(10x - 5 = 6x + 9\) \(10x + 6x = 9 - 5\) \(x = \dfrac{4}{16}\) (two errors in line 2)	M1 M0 A0ft
\(10x - 1 = 6x + 9\) \(10x - 6x = 9 + 1\) \(x = 3\) (exactly one error in line 1 but answer does not ft)	M0 M1 A0ft
\(7x - 6 = 6x + 9\) \(7x - 6x = 9 + 6\) \(x = 15\) (two errors in line 1)	M0 M1 A0ft
\(10x + 4 = 6x + 9\) \(10x - 6x = 9 + 4\) \(x = 3.25\) (neither M mark scored)	M0 M0 A0ft
\(10x - 5 = 30x + 45\)	M1M0A0ft
Any ft answer must be rounded or truncated to 1 dp or better
The last two marks can be implied without the collection of terms seen
eg \(10x - 1 = 6x + 9\) and \(x = 2.5\)	M0M1A1ft
Collecting terms before the bracket has been expanded	M0M0A0ft