Possible to solve for T? E=T-((0.3+(0.13T))
- Thread starter dan3213
- Start date
- Joined
- Feb 4, 2004
- Messages
- 16,583
Yes.
Please reply showing your efforts, so we can get started with helping you. Start from your first simplification (that is, the initial multiplications, etc, that got rid of the parentheses). Thank you!
The Highlander
Full Member
- Joined
- Feb 18, 2022
- Messages
- 937
Hint:-
Start by removing the red brackets
E = T - (0.3 + (0.13T))
(and then the green ones). Now you have three "separate" terms (two of them involving "T"), can you make a further "grouping" on the RHS so that there is now only one instance of "T"?
After that it should be a simple matter (of +/- & ×/÷) to transpose everything but the "T" to the LHS. ?
By "+/- & ×/÷" I, of course, mean "addition/subtraction & multiplication/division" (that was just too long to write into that sentence.)
Hope that helps. ?
The Highlander
Full Member
- Joined
- Feb 18, 2022
- Messages
- 937
Looks like another one we'll not hear from again, so, for the sake of completeness (and to help @Bruce understand the algebraic manipulation advice that was given ?).
E = T - (0.3 + (0.13T))
\(\displaystyle \implies\) E = T - 0.3 - (0.13T) (Removing the red brackets ())
\(\displaystyle \implies\) E = T - 0.3 - 0.13T (Removing the green brackets ())
\(\displaystyle \implies\) E = T - 0.13T - 0.3 (Rearranging the terms)
\(\displaystyle \implies\) E = T(1 - 0.13) - 0.3 (Grouping the T terms)
\(\displaystyle \implies\) E + 0.3 = T(1 - 0.13) (Adding 0.3 to both sides)
\(\displaystyle \implies\) E + 0.3 = 0.87T (Evaluating the (1 - 0.13) and removing its brackets)
\(\displaystyle \implies\) \(\displaystyle \sf\frac{E+0.3}{0.87}=T\) (Dividing both sides by 0.87)
E = T - (0.3 + (0.13T))
\(\displaystyle \implies\) E = T - 0.3 - (0.13T) (Removing the red brackets ())
\(\displaystyle \implies\) E = T - 0.3 - 0.13T (Removing the green brackets ())
\(\displaystyle \implies\) E = T - 0.13T - 0.3 (Rearranging the terms)
\(\displaystyle \implies\) E = T(1 - 0.13) - 0.3 (Grouping the T terms)
\(\displaystyle \implies\) E + 0.3 = T(1 - 0.13) (Adding 0.3 to both sides)
\(\displaystyle \implies\) E + 0.3 = 0.87T (Evaluating the (1 - 0.13) and removing its brackets)
\(\displaystyle \implies\) \(\displaystyle \sf\frac{E+0.3}{0.87}=T\) (Dividing both sides by 0.87)
And thus, \(\displaystyle \sf T=\frac{E+0.3}{0.87}\)
QED ?