Questions: Solve: (3r+5)/6 + 1 = (4r+3)/3.

Transcript text: Solve: $\frac{3 r+5}{6}+1=\frac{4 r+3}{3}$.

Solution

Solution Steps

Step 1: Eliminate the denominators

Multiply both sides of the equation by 6 to eliminate the denominators: \[ 6 \left( \frac{3r + 5}{6} + 1 \right) = 6 \left( \frac{4r + 3}{3} \right). \]

Step 2: Simplify both sides

Simplify the left and right sides of the equation: \[ (3r + 5) + 6 = 2(4r + 3). \]

Step 3: Expand and combine like terms

Expand the right side and combine like terms on the left side: \[ 3r + 5 + 6 = 8r + 6. \] \[ 3r + 11 = 8r + 6. \]

Step 4: Solve for $ r $

Subtract $ 3r $ from both sides and then subtract 6 from both sides: \[ 11 = 5r + 6. \] \[ 5 = 5r. \] Divide both sides by 5: \[ r = 1. \]

Final Answer

$\boxed{r = 1}$

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