Answer:
[tex]t=\dfrac{5m-4w}{8}[/tex]
Step-by-step explanation:
In general, in any "solve for" situation, you want to undo what is done to the variable of interest. Here, the variable is ...
- multiplied by 2
- has w added
- the sum is multiplied by 4
- and divided by 5
We want to undo these operations in reverse order. This can look like ...
[tex]m = \dfrac{4(2t+w)}{5} \qquad\text{given}\\\\5m=4(2t+w) \qquad\text{multiply by 5}\\\\5m=8t+4w \qquad\text{eliminate parentheses}\\\\5m-4w=8t \qquad\text{subtract 4w}\\\\t=\dfrac{5m-4w}{8} \qquad\text{divide by 8}[/tex]
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Note that we could have skipped the step "eliminate parentheses", but that would have resulted in a compound fraction for an answer. This way, we end with a simple rational expression.
