$\begin{align} &4\frac{1}{4}x-\frac{1}{2}x=24\\ &\frac{17}{4}x-\frac{2}{4}x=24\\ &\frac{15}{4}x=24&&\implies x=\frac{96}{14}\\ \end{align}$
Can anyone help me as I am not sure I got the right answer.
$\begin{align} &4\frac{1}{4}x-\frac{1}{2}x=24\\ &\frac{17}{4}x-\frac{2}{4}x=24\\ &\frac{15}{4}x=24&&\implies x=\frac{96}{14}\\ \end{align}$
Can anyone help me as I am not sure I got the right answer.
Assuming that "4(1/4)" is supposed to be the mixed fraction $4\!\frac{1}{4}$, then your reasoning and answer is correct, except that in the penultimate line, you wrote "$24x$" when you should just have $24$ (since you didn't multiply both sides by $x$), and that in the last line, you mean $\frac{96}{15}$, not $\frac{96}{14}$ (I assume this is just a typo). Finally, although it does not affect the correctness of your answer, you should also make sure to reduce your final result to lowest terms; neither $\frac{96}{14}$ nor $\frac{96}{15}$ is in lowest terms.