Question

5b/2-10=12+2b/3

Answer 1

To solve the equation \( \frac{5b}{2} - 10 = 12 + \frac{2b}{3} \), we can follow these steps:

1. Eliminate the fractions by finding a common denominator. The least common multiple of 2 and 3 is 6.

2. Multiply the entire equation by 6 to eliminate the fractions:

\[
6 \left( \frac{5b}{2} \right) - 6 \cdot 10 = 6 \cdot 12 + 6 \left( \frac{2b}{3} \right)
\]

This simplifies to:

\[
15b - 60 = 72 + 4b
\]

3. Now, rearrange the equation to isolate the \( b \) terms on one side and the constant terms on the other side. Subtract \( 4b \) from both sides:

\[
15b - 4b - 60 = 72
\]
\[
11b - 60 = 72
\]

4. Next, add 60 to both sides:

\[
11b = 72 + 60
\]
\[
11b = 132
\]

5. Now, divide both sides by 11:

\[
b = \frac{132}{11}
\]
\[
b = 12
\]

So, the solution to the equation is \( b = 12 \).