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 can start by simplifying both sides.

The intermediate steps can be as follows:

Step 1: Distribute 5 over 3 to both terms in the numerator: (5/3)x + 55/3 = -4/3

Step 2: Combine the like terms in the numerator: (5/3)x + 55/3 = -4/3

Step 3: Subtract 55/3 from both sides: (5/3)x = -4/3 - 55/3

Step 4: Combine the terms on the right side of the equation: (5/3)x = -59/3

Step 5: Divide both sides by 5/3: x = (-59/3)/(5/3)

Step 6: Simplify the division on the right side by multiplying by the reciprocal: x = (-59/3) * (3/5)

Step 7: Simplify the multiplication: x = -59/5

Therefore, the solution to the equation is x = -59/5.

Answer 2

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

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

Step 1: Start by simplifying the fractions on the left side of the equation.

To add the fractions, we need to find a common denominator. The common denominator for 3x and 3 is 3x.

So, we get (5 * 3)/(3x) + 11/3 = -4/3

Simplifying further, we have 15/(3x) + 11/3 = -4/3

Step 2: To combine the fractions with the same denominator, we add their numerators.

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

To add the fractions, we need a common denominator which is 3x.

So, we get (15 + (11 * x))/3x = -4/3

Step 3: Multiply both sides of the equation by the common denominator of 3x to eliminate the denominators.

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

Multiplying both sides by 3x, we get:

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

Simplifying,

15 + 11x = -4x

Step 4: Move all the terms involving x to one side of the equation.

15 + 11x + 4x = 0

15 + 15x = 0

Step 5: Solve for x.

15x = -15

Dividing both sides by 15, we get:

x = -1

So, the solution to the equation 5/(3x) + 11/3 = -4/3 is x = -1.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation 5/(3x) + 11/3 = -4/3, we need to get rid of the fractions by finding a common denominator and then solving for x.

Step 1: Find the common denominator
The denominators in the equation are 3x, 3, and 3. The common denominator is 3x since it includes both 3 and 3x.

Step 2: Multiply both sides of the equation by the common denominator
Multiply each term on both sides of the equation by 3x:
(5/(3x))(3x) + (11/3)(3x) = (-4/3)(3x)

Step 3: Simplify
On the left side of the equation, the 3x in the numerator and denominator will cancel out in the first term:
5 + (11/3)(3x) = (-4/3)(3x)

Simplify:
5 + 11x = -4x

Step 4: Combine like terms
Combine the x terms on the left side of the equation:
11x + 4x = -5

Combine like terms:
15x = -5

Step 5: Solve for x
Divide both sides of the equation by 15 to solve for x:
(15x)/15 = -5/15

Simplify:
x = -1/3

So the solution to the equation 5/(3x) + 11/3 = -4/3 is x = -1/3.