Exam-Style Problems

Stage 9 - Q1 - 2 marks

19227

Solve the equation.

\[2x+3=-7\]

Hint

Collect the \(x\) terms and constants on opposite sides.

Stage 9 - Q2 - 2 marks

19228

Solve the equation.

\[7x+3=3x+-9\]

Hint

Collect the \(x\) terms and constants on opposite sides.

Stage 9 - Q3 - 3 marks

19229

Solve the equation.

\[6(x-4)=-30\]

Hint

Collect the \(x\) terms and constants on opposite sides.

Stage 9 - Q4 - 3 marks

19230

Solve the equation.

\[8(x+5)=9x+(39)\]

Hint

Collect the \(x\) terms and constants on opposite sides.

Stage 9 - Q5 - 4 marks

19231

Solve efficiently and check.

\[6(x+5)=3(16)\]

Hint

A common numerical factor can be removed before expanding.

Stage 9 - Q6 - 4 marks

19232

Solve efficiently and check.

\[6(x+6)=3(22)\]

Hint

A common numerical factor can be removed before expanding.

Stage 9 - Q7 - 5 marks

19233

A learner expands \(7(x+7)\) as \(7x+7\). Explain the mistake and solve the equation.

\[7(x+7)=98\]

Hint

Distribute the outer coefficient to both terms.

Stage 9 - Q8 - 5 marks

19234

Solve the equation.

\[2x+7=8\]

Hint

Collect the \(x\) terms and constants on opposite sides.

Stage 9 - Q9 - 5 marks

19235

Find \(k\) so that \(x=6\) solves the equation.

\[4x+8=k\]

Hint

Here the solution value is given; the constant is unknown.

Stage 9 - Q10 - 3 marks

19236

Find \(k\) so that every real \(x\) solves the equation. For any other \(k\), find the only solution.

\[3(2x-5)-2(x+4)=kx-23\]

Hint

After collecting terms, consider when the coefficient of \(x\) becomes zero.