Solved on Dec 15, 2023

Solve the equation $(3x+8)(x+2)=0$ and write the answer in reduced fraction form.

STEP 1

Assumptions
1. We are given a quadratic equation in factored form: $(3x + 8)(x + 2) = 0$ .
2. We need to find the values of $x$ that satisfy the equation.
3. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 2

Apply the Zero Product Property to the given equation. This means that we can set each factor equal to zero and solve for $x$ .
$3x + 8 = 0 \quad \text{or} \quad x + 2 = 0$

STEP 3

Solve the first equation for $x$ .
$3x + 8 = 0$

STEP 4

Subtract 8 from both sides of the equation.
$3x = -8$

STEP 5

Divide both sides of the equation by 3 to isolate $x$ .
$x = \frac{-8}{3}$

STEP 6

Solve the second equation for $x$ .
$x + 2 = 0$

STEP 7

Subtract 2 from both sides of the equation.
$x = -2$

STEP 8

We have found the two solutions for $x$ .
The solutions to the equation $(3x + 8)(x + 2) = 0$ are $x = \frac{-8}{3}$ and $x = -2$ .

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Solve the equation $(3x+8)(x+2)=0$ and write the answer in reduced fraction form.

STEP 1

Assumptions
1. We are given a quadratic equation in factored form: $(3x + 8)(x + 2) = 0$ .
2. We need to find the values of $x$ that satisfy the equation.
3. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 2

Apply the Zero Product Property to the given equation. This means that we can set each factor equal to zero and solve for $x$ .
$3x + 8 = 0 \quad \text{or} \quad x + 2 = 0$

STEP 3

Solve the first equation for $x$ .
$3x + 8 = 0$

STEP 4

Subtract 8 from both sides of the equation.
$3x = -8$

STEP 5

Divide both sides of the equation by 3 to isolate $x$ .
$x = \frac{-8}{3}$

STEP 6

Solve the second equation for $x$ .
$x + 2 = 0$

STEP 7

Subtract 2 from both sides of the equation.
$x = -2$

STEP 8

We have found the two solutions for $x$ .
The solutions to the equation $(3x + 8)(x + 2) = 0$ are $x = \frac{-8}{3}$ and $x = -2$ .

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Solve the equation (3x+8)(x+2)=0(3x+8)(x+2)=0(3x+8)(x+2)=0 and write the answer in reduced fraction form.

STEP 1

STEP 2

Apply the Zero Product Property to the given equation. This means that we can set each factor equal to zero and solve for xxx.3x+8=0orx+2=03x + 8 = 0 \quad \text{or} \quad x + 2 = 03x+8=0orx+2=0

STEP 3

Solve the first equation for xxx.3x+8=03x + 8 = 03x+8=0

STEP 4

Subtract 8 from both sides of the equation.3x=−83x = -83x=−8

STEP 5

Divide both sides of the equation by 3 to isolate xxx.x=−83x = \frac{-8}{3}x=3−8​

STEP 6

Solve the second equation for xxx.x+2=0x + 2 = 0x+2=0

STEP 7

Subtract 2 from both sides of the equation.x=−2x = -2x=−2

STEP 8

We have found the two solutions for xxx.The solutions to the equation (3x+8)(x+2)=0(3x + 8)(x + 2) = 0(3x+8)(x+2)=0 are x=−83x = \frac{-8}{3}x=3−8​ and x=−2x = -2x=−2.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the equation $(3x+8)(x+2)=0$ and write the answer in reduced fraction form.

Apply the Zero Product Property to the given equation. This means that we can set each factor equal to zero and solve for $x$ .
$3x + 8 = 0 \quad \text{or} \quad x + 2 = 0$

Solve the first equation for $x$ .
$3x + 8 = 0$

Subtract 8 from both sides of the equation.
$3x = -8$

Divide both sides of the equation by 3 to isolate $x$ .
$x = \frac{-8}{3}$

Solve the second equation for $x$ .
$x + 2 = 0$

Subtract 2 from both sides of the equation.
$x = -2$

We have found the two solutions for $x$ .
The solutions to the equation $(3x + 8)(x + 2) = 0$ are $x = \frac{-8}{3}$ and $x = -2$ .