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 5 over 3x + 11 over 3 = −4 over 3, we need to isolate the variable x.

First, subtract 11 over 3 from both sides to get:

5 over 3x = -4 over 3 - 11 over 3

Simplifying the right side:

5 over 3x = -15 over 3

Now, multiply both sides by 3 to eliminate the fractions:

3 * (5 over 3x) = 3 * (-15 over 3)

This simplifies to:

5 over x = -15

To solve for x, we can cross-multiply:

5 * x = -15 * 1

This becomes:

5x = -15

Finally, divide both sides by 5 to solve for x:

x = -15/5

Simplifying:

x = -3

Therefore, the solution to the equation is x = -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: Combine the fraction terms on the left side of the equation:
(5/3x) + (11/3) = -4/3

Step 2: Find a common denominator for the fractions on the left side, which is 3x:
(5/3x) + (11/3) = -4/3

Step 3: Multiply the first fraction by (3/3) to get a common denominator:
(5/3x)(3/3) + (11/3) = -4/3

Simplifying the fractions:
(15/9x) + (11/3) = -4/3

Step 4: Combine the fractions on the left side of the equation:
(15/9x) + (11/3) = -4/3

Step 5: Multiply the first fraction by (1/3) to get a common denominator:
(15/9x)(1/3) + (11/3) = -4/3

Simplifying the fractions:
(15/27x) + (11/3) = -4/3

Step 6: Combine the fractions on the left side of the equation:
(15/27x) + (11/3) = -4/3

Step 7: Multiply the first fraction by (3/3) to get a common denominator:
(15/27x)(3/3) + (11/3) = -4/3

Simplifying the fractions:
(45/81x) + (11/3) = -4/3

Step 8: Combine the fractions on the left side of the equation:
(45/81x) + (11/3) = -4/3

Step 9: Multiply the second fraction by (27/27) to get a common denominator:
(45/81x) + (11/3)(27/27) = -4/3

Simplifying the fractions:
(45/81x) + (297/81) = -4/3

Step 10: Combine the fractions on the left side of the equation:
(45/81x) + (297/81) = -4/3

Step 11: To eliminate fractions, multiply each term of the equation by 81:
(81)(45/81x) + (81)(297/81) = (81)(-4/3)

Simplifying the equation:
45x + 297 = -108

Step 12: Solve for x:
45x + 297 = -108

Subtract 297 from both sides of the equation:
45x = -108 - 297

Simplifying the equation:
45x = -405

Step 13: Divide both sides of the equation by 45 to solve for x:
x = -405/45

Simplifying the expression:
x = -9

Therefore, the solution to the equation (5/3x) + (11/3) = -4/3 is x = -9.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation 5/(3x) + 11/3 = -4/3, we need to find the value of x that satisfies the equation. Let's go step by step to solve it:

Step 1: Start by simplifying the equation.
To add fractions, we need a common denominator. In this case, the common denominator is 3x. So, we can rewrite the equation as follows:
(5/3x) + (11/3) = (-4/3)

Step 2: Get rid of the fractions by multiplying every term by the common denominator.
Multiply both sides of the equation by 3x:
3x * (5/3x) + 3x * (11/3) = 3x * (-4/3)

Simplifying, we get:
5 + (11x/3) = -4

Step 3: Move all the terms involving x to one side of the equation.
Subtract 5 from both sides of the equation:
5 + (11x/3) - 5 = -4 - 5

The 5's on the left side cancel out, and we have:
11x/3 = -9

Step 4: Isolate x by multiplying both sides of the equation by the reciprocal of the coefficient of x.
Multiply both sides of the equation by 3/11:
(3/11) * (11x/3) = (3/11) * (-9)

The 11x/3 on the left side cancels out, and we have:
x = -27/11

So, the solution to the equation 5/(3x) + 11/3 = -4/3 is x = -27/11.