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.

5 over 3x = ?

x = ?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we can start by subtracting 11/3 from both sides of the equation:

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

5/(3x) = -15/3

Next, we can simplify -15/3:

5/(3x) = -5

To isolate x, we can multiply both sides of the equation by (3/5):

(3/5)(5/(3x)) = (3/5)(-5)

1/x = -3/5

Finally, to solve for x, we can take the reciprocal on both sides:

x = 5/(-3)

x = -5/3

Answer 2

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

To solve the equation 5 over 3x + 11 over 3 = −4 over 3, we need to simplify the left side of the equation first.

Step 1: Simplify 11 over 3.
11 over 3 = 11/3

Step 2: Combine 5 over 3x and 11 over 3.
5 over 3x + 11/3 = (5/3x + 11/3)

Step 3: Equate the combined expression to -4 over 3.
(5/3x + 11/3) = -4/3

Now, let's solve for x.

Step 4: Multiply both sides of the equation by the common denominator, which is 3.
3 * (5/3x + 11/3) = 3 * (-4/3)
15/3x + 33/3 = -12/3

Step 5: Simplify the equation.
5/x + 11 = -4

Step 6: Subtract 11 from both sides of the equation.
5/x = -4 - 11
5/x = -15

Step 7: Multiply both sides of the equation by x to solve for x.
x * (5/x) = x * (-15)
5 = -15x

Step 8: Divide both sides of the equation by -15 to isolate x.
5/-15 = -15x/-15
-1/3 = x

So, the equation 5 over 3x + 11 over 3 = −4 over 3 is solved as follows:

The equation becomes 5/x + 11 = -4
Subtracting 11 from both sides, we get 5/x = -15
Multiplying both sides by x, we get x = -1/3

Answer 3

[AI-generated answer — Explain Bot]

To solve the given equation, let's follow the steps:

Step 1: Begin by subtracting 11/3 from both sides of the equation. This will isolate the term containing 'x' on one side.

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

Simplifying the equation:

5/3x = -15/3

Step 2: Now, multiply both sides of the equation by the reciprocal of 5/3 to solve for 'x'. The reciprocal is found by swapping the numerator and the denominator of 5/3.

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

Simplifying the equation:

1x = -45/15

x = -3

So, the solution to the equation is x = -3.

Final Solution:

5 over 3x = -15/3
x = -3