Easy -1.8 This is a straightforward linear inequality requiring only basic algebraic manipulation: multiply through by 7, collect like terms, and divide. It's a routine procedural question with no conceptual challenges, making it significantly easier than average A-level content.
for correctly multiplying by 7 to eliminate the fraction, including expanding bracket if this step done first
\(x < \frac{12}{10}\) or \(x < \frac{6}{5}\) oe isw or ft
M1
for correctly collecting \(x\) terms on one side and number terms on the other and simplifying
\(x < 1.2\) or \(x < \frac{6}{5}\) oe isw or ft
M1
ft their \(ax\) [inequality] \(b\), where \(b \neq 0\) and \(a \neq 0\) or \(\pm 1\)
[3]
Guidance notes:
- may be earned later; the first two Ms may be earned with an equation or wrong inequality
- ft wrong first step
- award 3 marks only if correct answer obtained after equations or inequalities are used with no errors
Question 1:
$\frac{1}{4}x - 5 > 14x + 7$
$12 > 10x$ or $10x < 12$ or ft | M1 | for correctly multiplying by 7 to eliminate the fraction, including expanding bracket if this step done first
$x < \frac{12}{10}$ or $x < \frac{6}{5}$ oe isw or ft | M1 | for correctly collecting $x$ terms on one side and number terms on the other and simplifying
$x < 1.2$ or $x < \frac{6}{5}$ oe isw or ft | M1 | ft their $ax$ [inequality] $b$, where $b \neq 0$ and $a \neq 0$ or $\pm 1$
[3]
Guidance notes:
- may be earned later; the first two Ms may be earned with an equation or wrong inequality
- ft wrong first step
- award 3 marks only if correct answer obtained after equations or inequalities are used with no errors