# Solve for t 2+1/3t=1+1/4t 2+13t=1+14t
Combine 13 and t.
2+t3=1+14t
Combine 14 and t.
2+t3=1+t4
Move all terms containing t to the left side of the equation.
Subtract t4 from both sides of the equation.
2+t3-t4=1
To write t3 as a fraction with a common denominator, multiply by 44.
2+t3⋅44-t4=1
To write -t4 as a fraction with a common denominator, multiply by 33.
2+t3⋅44-t4⋅33=1
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply t3 and 44.
2+t⋅43⋅4-t4⋅33=1
Multiply 3 by 4.
2+t⋅412-t4⋅33=1
Multiply t4 and 33.
2+t⋅412-t⋅34⋅3=1
Multiply 4 by 3.
2+t⋅412-t⋅312=1
2+t⋅412-t⋅312=1
Combine the numerators over the common denominator.
2+t⋅4-t⋅312=1
Simplify each term.
Simplify the numerator.
Factor t out of t⋅4-t⋅3.
Factor t out of t⋅4.
2+t(4)-t⋅312=1
Factor t out of -t⋅3.
2+t(4)+t(-1⋅3)12=1
Factor t out of t(4)+t(-1⋅3).
2+t(4-1⋅3)12=1
2+t(4-1⋅3)12=1
Multiply -1 by 3.
2+t(4-3)12=1
Subtract 3 from 4.
2+t⋅112=1
2+t⋅112=1
Multiply t by 1.
2+t12=1
2+t12=1
2+t12=1
Move all terms not containing t to the right side of the equation.
Subtract 2 from both sides of the equation.
t12=1-2
Subtract 2 from 1.
t12=-1
t12=-1
Multiply both sides of the equation by 12.
12⋅t12=12⋅-1
Simplify both sides of the equation.
Cancel the common factor of 12.
Cancel the common factor.
12⋅t12=12⋅-1
Rewrite the expression.
t=12⋅-1
t=12⋅-1
Multiply 12 by -1.
t=-12
t=-12
Solve for t 2+1/3t=1+1/4t

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