Q. 423 - Intermediate Algebra

Question

Use the Zero Product Property in following exercises and solve.

$(5b+1)(6b+1)=0$

Step-by-Step Solution

Answer

The solution of the given expression are $b=\frac{-1}{5}and \frac{-1}{6}$.

Step 1. Given and explanation.

We have $(5b+1)(6b+1)=0$

We know that the zero product property states that if , then either of the factors, both are equal t zero.

So putting them equal to zero will give us the values.

Step 2. Evaluating the values.

We have $(5b+1)(6b+1)=0$

Putting them equal to zero gives us,

1. $$\begin{gathered} 5b+1=0 \\ 5b=-1 \\ b=\frac{-1}{5} \end{gathered}$$
   
2. $$\begin{gathered} 6b+1=0 \\ 6b=-1 \\ b=\frac{-1}{6} \end{gathered}$$
   

This shows that values are $\frac{-1}{5} and \frac{-1}{6}$.

Step 3. Check the solution.

We will check the solution by putting the value of the solution in the equation separately. If the equation satisfies, our answer is right.

1. When $b=\frac{-1}{5}$
   $$\begin{gathered} \left[(5\times \frac{-1}{5})+1\right]\left[(6\times \frac{-1}{5})+1\right]=0 \\ \left[-1+1\right]\left[\frac{-6}{5}+1\right]=0 \\ \left(0\right)\left(\frac{-1}{5}\right)=0 \\ 0=0 \end{gathered}$$
   Hence satisfied.
2. When $b=\frac{-1}{6}$
   $$\begin{gathered} \left[(5\times \frac{-1}{6})+1\right]\left[(6\times \frac{-1}{6})+1\right]=0 \\ \left[\frac{-5}{6}+1\right]\left[-1+1\right]=0 \\ \left(\frac{1}{5}\right)\left(0\right)=0 \\ 0=0 \end{gathered}$$
   Hence satisfied.

Thus our calculations are right.