Question

Solve for j.

(j + 1)(j + 7) = 0

Write your answers as integers or as proper or improper fractions in simplest form.

j =
or j =

Answer 1

To solve the equation \((j + 1)(j + 7) = 0\), we can apply the zero product property. This property states that if the product of two expressions is zero, then at least one of the expressions must be zero.

We can set each factor equal to zero:

1. \(j + 1 = 0\)
2. \(j + 7 = 0\)

Now we solve each equation:

1. For \(j + 1 = 0\):
\[
j = -1
\]

2. For \(j + 7 = 0\):
\[
j = -7
\]

Thus, the solutions for \(j\) are:
\[
j = -1 \quad \text{or} \quad j = -7
\]

So, the final answers are:
\[
j = -1 \quad \text{or} \quad j = -7
\]