Question

Solve m
m= 4/5 (2t+w) for t

Answer 1

Is this rearranging formulae? Because, if so-



m=4 (2t+w)
5





m(2t+w)=4
5




4 divide m= 2t+w
5




(4 divide m) - w all over 2
(5

Answer 2

`t=(5m-4w)/(8)`

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 ...

`m = (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=(5m-4w)/(8) \qquad\text{divide by 8}`

_____

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.