6) \( \frac{7}{b+5}=\frac{10}{5} \)

To solve the equation \( \frac{7}{b+5}=\frac{10}{5} \), we first simplify the right side. Since \( \frac{10}{5} = 2 \), the equation becomes \( \frac{7}{b+5} = 2 \). Next, we cross-multiply to eliminate the fraction: \( 7 = 2(b + 5) \). Expanding the right side gives \( 7 = 2b + 10 \). Now, let's isolate \( b \). Subtract 10 from both sides: \( 7 - 10 = 2b \), which simplifies to \( -3 = 2b \). Dividing both sides by 2, we find \( b = -\frac{3}{2} \) or \( b = -1.5 \). So, the solution to the equation is \( b = -1.5 \). Checking our solution, if we substitute \( b = -1.5 \) back into the original equation, we have \( \frac{7}{-1.5 + 5} = \frac{7}{3.5} = 2 \), confirming that it holds true!