Hint
Use the stated units and precision. Subtract the constant from all three expressions, divide by the negative coefficient and reverse both inequalities.
Worked solution
(a)
Subtracting 8 gives \(-4\le -2x<2\). Division by -2 reverses the signs, giving \(-1<x\le 2\).
Answer: \(-1<x\le 2\)
(b)
The lower boundary is strict while the upper boundary includes equality.
Answer: \(-1<x\le 2\); open at -1, filled at 2.
(c)
Subtract the constant from all three expressions, divide by the negative coefficient and reverse both inequalities.
\(3\)
Answer: \(3\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 3 marks
- 1 mark: Apply the same subtraction to all three parts.
- 1 mark: Reverse both inequality signs on division by the negative coefficient and retain their strictness.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Translate the solved interval to the correct open/closed endpoint drawing.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Subtract the constant from all three expressions, divide by the negative coefficient and reverse both inequalities.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 7 marks.