Although possible, the question does not ask us to work out the solutions to the equation, only whether Kelly's values are correct.
So substitute her values into the left-hand side of the expression, evaluate them and compare to 2.

For w = 1:

$\begin{array}{rcl} 3 w - w^{3} & = & 3 (1) - {(1)}^{3} \\ = & 3 - 1 \\ = & 2 ✓ \end{array}$

[1]

For w = -1:

$\begin{array}{rcl} 3 w - w^{3} & = & 3 (- 1) - {(- 1)}^{3} \\ = & - 3 - (- 1) \\ = & - 3 + 1 \\ = & - 2 \times \end{array}$

Only one of Kelly's values for w, w = 1, is correct; w = -1 is incorrect [1]
The correct solutions to the equation are w = 1 and w = -2.

Algebra Toolkit (Cambridge O Level Maths)

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