(b) Write down the inequality represented by the number line. [2 marks]
Mark scheme (a)
Answer
Mark
Comments
\(5x - 3x\) or \(2x\) or \(3x - 5x\) or \(-2x\) or \(15 - 6\) or 9 or \(6 - 15\) or \(-9\)
M1
may be seen as an annotation to the given inequality eg \(-\ 6\) written under \(+\ 15\)
\(2x \gt 9\) or \(-9 \gt -2x\) or 4.5 or \(\dfrac{9}{2}\) or \(4\dfrac{1}{2}\)
A1
implied by correct answer
\(x \gt 4.5\) or \(x \gt \dfrac{9}{2}\) or \(x \gt 4\dfrac{1}{2}\)
A1ft
ft solution of inequality of the form \(2x \gt k\) where \(k\) is a number or \(m \gt -2x\) where \(m\) is a number or \(ax \gt 9\) where \(a\) is an integer not equal to 1 or \(-9 \gt bx\) where \(b\) is an integer not equal to 1
Additional guidance
In all cases accept the inequality written correctly in reverse order For example, for \(2x \gt 9\) accept \(9 \lt 2x\)
\(4.5 \lt x\)
M1A1A1
\(2x \gt 21\), \(x \gt 10.5\)
M1A0A1ft
\(8x \gt 9\), \(x \gt 1.125\)
M1A0A1ft
Do not allow a correct answer in working followed by an incorrect answer on the answer line eg \(x \gt \dfrac{9}{2}\) in working with 4.5 on the answer line
M1A1A0
Do not allow the correct answer with another answer eg \(x \gt 4.5\) and \(x = 4.5\) on the answer line
M1A1A0
Mark scheme (b)
Answer
Mark
Comments
\(2 \leqslant x \lt 5\) or \(5 \gt x \geqslant 2\)
B2
any letter B1 \(2 \leqslant x\) or \(x \geqslant 2\) or \(x \lt 5\) or \(5 \gt x\) SC1 \(2 \lt x \leqslant 5\) or \(5 \geqslant x \gt 2\)
