Question

Solve the following equation and check your results: $2y+\frac{5}{3}=\frac{26}{3}-y$

Answer 1

Step 1: Calculate the value of $y$.

Cross multiply the terms, take the similar terms on one side and then calculate the value of $y$.

Therefore,

$\begin{array}{c}2y+\frac{5}{3}=\frac{26}{3}-y\\ 2y+y=\frac{26}{3}-\frac{5}{3}\\ 3y=\frac{21}{3}\\ 3y=7\\ y=\frac{7}{3}\end{array}$

Step 2: Verify the equation for $y=\frac{7}{3}$.

Apply $y=\frac{7}{3}$in the equation $2y+\frac{5}{3}=\frac{26}{3}-y$.

Solve LHS.

$\begin{array}{c}2\times \frac{7}{3}+\frac{5}{3}=\frac{14}{3}+\frac{5}{3}\\ =\frac{19}{3}\end{array}$

Solve RHS.

$\frac{26}{3}-\frac{7}{3}=\frac{19}{3}$

Therefore, LHS is equal to RHS.

Hence, the value of $y$is verified for the equation $2y+\frac{5}{3}=\frac{26}{3}-y$ and the value is $\frac{7}{3}$.