Hint
Use the stated units and precision. Exclude both denominator zeros, cross-multiply whole factors and substitute the resulting candidate into the original equation.
Worked solution
(a)
\(6(x-9)=7(x-2)\) gives \(\displaystyle x=-40\). It differs from both excluded values and both original fractions equal \(\displaystyle - \frac{1}{7}\).
Answer: \(x=-40,\quad x\ne 2,9\)
(b)
Exclude both denominator zeros, cross-multiply whole factors and substitute the resulting candidate into the original equation.
\(-42\)
Answer: \(-42\)
(c)
Exclude both denominator zeros, cross-multiply whole factors and substitute the resulting candidate into the original equation.
\(\displaystyle - \frac{1}{7}\)
Answer: \(\displaystyle - \frac{1}{7}\)
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: Clear both nonzero denominators and solve the resulting linear equation.
- 1 mark: Check the candidate against both original denominator restrictions.
- 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: Exclude both denominator zeros, cross-multiply whole factors and substitute the resulting candidate into the original equation.
- 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: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Exclude both denominator zeros, cross-multiply whole factors and substitute the resulting candidate into the original equation.
- 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.