Question

Solve$\frac{3r+5}{6}+1=\frac{4r+3}{3}$

Short answer

The answer is$r=1$

Step-by-step solution

Step 1. Given information

The equation is $\frac{3r+5}{6}+1=\frac{4r+3}{3}$

Find value of r and check it.

Step 2. Calculation

Simplify the equation $\frac{3r+5}{6}+1=\frac{4r+3}{3}$

LCD of 3,6 is 6. so,

$$\begin{gathered} 6\left(\frac{3r+5}{6}+1\right)=6\left(\frac{4r+3}{3}\right) \\ 3r+5+6=8r+6 \end{gathered}$$

Combine like terms,

$$\begin{gathered} 5+6-6=8r-3r \\ 5=5r \\ 1=r \end{gathered}$$

Step 3. Check the answer

Substitute $r=1$in equation $\frac{3r+5}{6}+1=\frac{4r+3}{3}$

$$\begin{gathered} \frac{3\left(1\right)+5}{6}+1=\frac{4\left(1\right)+3}{3} \\ \frac{8}{6}+1=\frac{7}{3} \\ \frac{7}{3}=\frac{7}{3} \end{gathered}$$