Solve |f(x)| = |g(x)| with non-linear or exponential expressions

Solve modulus equation where at least one expression inside the modulus is non-linear or exponential, e.g. |x³-14| = 13 or |2^x - 7| = 1.

4 questions · Moderate -0.3

1.02l Modulus function: notation, relations, equations and inequalities
Sort by: Default | Easiest first | Hardest first
CAIE P2 2012 June Q1
4 marks Moderate -0.3
1 Solve the equation \(\left| x ^ { 3 } - 14 \right| = 13\), showing all your working.
CAIE P2 2013 June Q1
5 marks Moderate -0.3
1 Solve the equation \(\left| 2 ^ { x } - 7 \right| = 1\), giving answers correct to 2 decimal places where appropriate.
CAIE P3 2012 June Q1
3 marks Moderate -0.3
1 Solve the equation \(\left| 4 - 2 ^ { x } \right| = 10\), giving your answer correct to 3 significant figures.
CAIE P2 2018 November Q1
5 marks Moderate -0.3
  1. Solve the equation \(|9x - 2| = |3x + 2|\). [3]
  2. Hence, using logarithms, solve the equation \(|3^{x+2} - 2| = |3^{x+1} + 2|\), giving your answer correct to 3 significant figures. [2]