Question

The equation 5 over 3x+11 over 3=−4 over 3

is solved as follows. Fill in the correct numbers to complete the solution.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we start by simplifying the expression on the left side:

So we have:

(5/(3x)) + (11/3) = -4/3

Next, we need to get rid of the fraction. We can do this by multiplying every term by the least common denominator (3x). So we have:
3x * (5/(3x)) + 3x * (11/3) = 3x * (-4/3)

Simplifying each term gives:
5 + 11x = -4x

Now, we can combine like terms:
11x + 4x = -5

Adding the x terms gives:
15x = -5

To solve for x, we divide both sides by 15:
x = -5/15

Simplifying the fraction gives:
x = -1/3

Therefore, the solution to the equation is x = -1/3.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation 5/(3x) + 11/3 = -4/3, follow these steps:

Step 1: Multiply every term in the equation by the common denominator, which is 3.

3 * 5/(3x) + 3 * 11/3 = 3 * -4/3

Step 2: Simplify each term.

15/(3x) + 11 = -4

Step 3: Move 11 from the left side to the right side of the equation by subtracting it from both sides.

15/(3x) = -4 - 11

15/(3x) = -15

Step 4: Multiply both sides of the equation by 3x to isolate the variable.

(3x) * (15/(3x)) = -15 * (3x)

15 = -45x

Step 5: Divide both sides of the equation by -45 to solve for x.

15 / -45 = x

x = -1/3

Therefore, the solution to the equation is x = -1/3.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation (5/(3x)) + (11/3) = -4/3, we need to isolate the variable x.

First, let's simplify the equation by finding a common denominator for the fractions. The common denominator for 3x, 3, and -4 is 3x, so we can rewrite the equation as:

(5/(3x)) + (11/3) = (-4/(3x))

Next, we can combine the fractions on the left side of the equation by finding a common denominator of 3x:

((5 * 3) + (11 * x)) / (3x) = (-4/(3x))

Simplifying the numerator:

(15 + 11x) / (3x) = (-4/(3x))

Now, we can remove the denominators by cross-multiplying:

(15 + 11x) * 3x = -4

Expanding:

45x + 33x^2 = -4

Rearranging the equation to bring it to a standard quadratic form:

33x^2 + 45x + 4 = 0

Now, to solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 33, b = 45, and c = 4. Substituting these values into the quadratic formula:

x = (-(45) ± √((45)^2 - 4(33)(4))) / (2(33))

Calculating the discriminant:

√((45)^2 - 4(33)(4)) = √(2025 - 528) = √1497 ≈ 38.67

Solving for x using both the positive and negative roots:

x = (-(45) + 38.67) / (2(33)) ≈ -0.22
x = (-(45) - 38.67) / (2(33)) ≈ -3.04

So, the two solutions to the equation are approximately x = -0.22 and x = -3.04.