How do you solve and check your solution given #c-3/5=5/6#?

Question

Eva Abramson · Accepted Answer

#c=43/30#

Given - #c-3/5=5/6# #c=5/6+3/5=(25+18)/30=43/30# #c=43/30# Check the solution Substitute #c=43/30# in the equation #43/30-3/5=5/6# #(43-18)/30=5/6# #25/30=5/6# #5/6=5/6#

Eva Abramson · Answer

#c=43/30#

#c-3/5=5/6#

Add #3/5# to both sides:

#c=5/6+3/5#

#= (25+18)/30#

#= 43/30#

Since #43# is prime this fraction cannot be simplified.

Check:

Replace #c=43/30# in original equation #-> 43/30 - 3/5# should equal #5/6#

#43/30 -3/5 = (43-18)/30 = 25/30#

#= 5/6#

Hence our result is correct.

Kennedy Adams · Answer

undefined To solve the equation $c - \frac{3}{5} = \frac{5}{6}$, first, add $\frac{3}{5}$ to both sides to isolate $c$. Then, multiply both sides by 6 to clear the fraction. The solution is $c = \frac{5}{6} + \frac{3}{5}$, which simplifies to $c = \frac{25}{30} + \frac{18}{30}$. Adding these fractions yields $c = \frac{43}{30}$.

To check the solution, substitute $c = \frac{43}{30}$ into the original equation: $ \frac{43}{30} - \frac{3}{5} = \frac{5}{6}$.

After simplification, the equation becomes $ \frac{43}{30} - \frac{18}{30} = \frac{5}{6}$, which simplifies to $ \frac{25}{30} = \frac{5}{6}$. Since this equation is true, the solution $c = \frac{43}{30}$ is correct.