Question

Solve the equation using the Zero Product Property. (3x + 1)(x – 5) = 0

• and 5
• and –5
• and 5
• and –5

Answer 1

3 x + 1 = 0 Subtract 1 from both sides

3 x + 1 - 1 = 0 - 1

3 x = - 1 Divide both sides by 3

3 x / 3 = - 1 / 3

x = - 1 / 3

x – 5 = 0 Add 5 from both sides

x - 5 + 5 = 0 + 5

x = 5

The solutions are :

- 1 / 3 and 5

Answer 2

Thanks

Answer 3

(n-5)(n+3)=0

Answer 4

[AI-generated answer — Clown Bot]

Well, well, well. Looks like we have quite the equation here. Let's put the Zero Product Property to good use, shall we?

According to this property, if the product of two factors is equal to zero, then at least one of the factors must be zero. So, to solve the equation (3x + 1)(x – 5) = 0, we just need to set each factor equal to zero and solve for x.

First, let's set 3x + 1 equal to zero:
3x + 1 = 0

Solving for x, we get:
3x = -1
x = -1/3

Now, let's set x – 5 equal to zero:
x – 5 = 0

Solving for x, we get:
x = 5

So, the solutions to the equation (3x + 1)(x – 5) = 0 are x = -1/3 and x = 5.

Answer 5

[AI-generated answer — Explain Bot]

To solve the equation (3x + 1)(x – 5) = 0 using the Zero Product Property, we need to find the values of x that make either of the two factors equal to zero. According to the Zero Product Property, if the product of two real numbers is equal to zero, then at least one of the numbers must be zero.

So, let's set each factor equal to zero and solve for x:

1) 3x + 1 = 0:
Subtract 1 from both sides: 3x = -1
Divide both sides by 3: x = -1/3

2) x - 5 = 0:
Add 5 to both sides: x = 5

Therefore, the equation (3x + 1)(x – 5) = 0 has two solutions:
- x = -1/3,
- x = 5.

So, the correct options are "and 5" and "and -1/3".