In this question you must show all stages of your working - Edexcel - A-Level Maths Pure - Question 2 - 2022 - Paper 2

After obtaining the values from both cases, we should verify the solutions by substituting them back into the original absolute equation.

1. For $x = -\frac{4}{3}$:

   • Substitute into $|3 - 2(-\frac{4}{3})|$: $|3 + \frac{8}{3}| = |\frac{9}{3} + \frac{8}{3}| = |\frac{17}{3}| = \frac{17}{3}$
     Compare with $7 + (-\frac{4}{3}) = \frac{21}{3} - \frac{4}{3} = \frac{17}{3}$.
   • This solution is valid.

2. For $x = -10$:

   • Substitute into $|3 - 2(-10)|$: $|3 + 20| = |23| = 23$
     Compare with $7 + (-10) = -3$, which does not equal 23.
   • This solution is invalid.

Thus, the only valid solution to the equation $|3 - 2x| = 7 + x$ is:

$x = -\frac{4}{3}$