To solve the equation \((x - 1)(2x + 5) = 0\), we can use the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero.

Question

This gives us two separate equations to solve:

1. \(x - 1 = 0\)
2. \(2x + 5 = 0\)

Now, we'll solve each equation:

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

2. For \(2x + 5 = 0\):
\[
2x = -5 \\
x = -\frac{5}{2}
\]

So, the values of \(x\) that make the equation equal to 0 are:
\[
x = 1 \quad \text{and} \quad x = -\frac{5}{2}
\]\
make this like a 6th grader wrote this

Answer 1

To solve the equation \((x - 1)(2x + 5) = 0\), we can use a rule called the Zero Product Property. This rule tells us that if we have two things multiplied together (like our equation) that equal zero, then at least one of those things has to be zero too.

So we can break it down into two smaller equations:

1. \(x - 1 = 0\)
2. \(2x + 5 = 0\)

Now, let's solve each of these equations one by one.

1. For the first equation, \(x - 1 = 0\):

   • To find \(x\), we just add 1 to both sides. \[ x = 1 \]

2. For the second equation, \(2x + 5 = 0\):

   • First, we want to get \(2x\) by itself. So, we subtract 5 from both sides. \[ 2x = -5 \]
   • Now we divide both sides by 2 to solve for \(x\). \[ x = -\frac{5}{2} \]

So, the two values of \(x\) that make the equation equal to zero are: \[ x = 1 \quad \text{and} \quad x = -\frac{5}{2} \]

And that's it! We found the answers!