Question

solve for b.\\(\frac{b - 5}{10} = \frac{b + 1}{6}\\)

Explanation:

Step1: Cross - multiply the fractions

To eliminate the fractions, we use the cross - multiplication property. If $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$. So for $\frac{b - 5}{10}=\frac{b + 1}{6}$, we get $6(b - 5)=10(b + 1)$.

Step2: Expand both sides

Using the distributive property $a(b + c)=ab+ac$, we expand the left - hand side: $6b-30$ and the right - hand side: $10b + 10$. So the equation becomes $6b-30 = 10b+10$.

Step3: Move the terms with b to one side and constants to the other

Subtract $6b$ from both sides: $6b-6b - 30=10b-6b + 10$, which simplifies to $-30 = 4b+10$. Then subtract 10 from both sides: $-30-10=4b+10 - 10$, so $-40 = 4b$.

Step4: Solve for b

Divide both sides by 4: $\frac{-40}{4}=\frac{4b}{4}$, which gives $b=-10$.

Answer:

$b = - 10$