Question

What is the solution of the equation 8/9(x+12)=32/3 when solving for x ?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for x, we need to isolate the variable x on one side of the equation. We can do this by performing the following steps:

1. Multiply both sides of the equation by 9 to eliminate the denominator of the left side: (8/9)(x + 12) * 9 = (32/3) * 9,
which simplifies to: 8(x + 12) = 96.

2. Distribute 8 to the terms inside the parentheses on the left side of the equation: 8x + 96 = 96.

3. Subtract 96 from both sides of the equation to isolate the x term: 8x + 96 - 96 = 96 - 96,
which simplifies to: 8x = 0.

4. Divide both sides of the equation by 8 to solve for x: (8x)/8 = 0/8,
which simplifies to: x = 0.

Therefore, the solution of the equation 8/9(x+12) = 32/3 when solving for x is x = 0.

Answer 2

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

To find the solution for x in the equation (8/9)(x + 12) = 32/3, we can follow these steps:

Step 1: Distribute 8/9 to the terms inside the parentheses:
(8/9)(x + 12) = 32/3
(8/9)x + (8/9)(12) = 32/3

Step 2: Simplify the expression (8/9)(12):
(8/9)x + 96/9 = 32/3

Step 3: Simplify the fractions on both sides of the equation:
(8/9)x + 10⅔ = 10⅔

Step 4: Subtract 10⅔ from both sides of the equation to isolate the x term:
(8/9)x = 10⅔ - 10⅔
(8/9)x = 0

Step 5: To solve for x, multiply both sides of the equation by the reciprocal of 8/9, which is 9/8:
(9/8)(8/9)x = 0 * (9/8)
x = 0

Therefore, the solution for x is x = 0.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation (8/9)(x + 12) = 32/3 for x, we can follow these steps:

1. Multiply both sides of the equation by the reciprocal of 8/9, which is 9/8. This will help us isolate the variable x.
(8/9)(x + 12) * (9/8) = (32/3) * (9/8)
(x + 12) = (36/1)

2. To remove the parentheses, we will distribute 9/8 to both terms inside.
(x + 12) * (9/8) = 36/1

3. Multiply x by 9/8.
(9/8)x + (9/8)(12) = 36/1

4. Simplify the equation.
(9/8)x + (108/8) = 36/1

5. Combine the fractions on the left side.
(9/8)x + 108/8 = 36/1

6. Convert the right side fraction into a fraction over 8.
(9/8)x + 108/8 = 288/8

7. Now our equation is:
(9/8)x + 108/8 = 288/8

8. Subtract 108/8 from both sides of the equation to isolate x.
(9/8)x + (108/8) - (108/8) = (288/8) - (108/8)
(9/8)x = 180/8

9. Simplify the right side fraction.
(9/8)x = 22.5

10. Multiply both sides of the equation by the reciprocal of (9/8), which is 8/9.
(9/8)x * (8/9) = 22.5 * (8/9)
x = 20

Therefore, the solution to the equation (8/9)(x + 12) = 32/3 when solving for x is x = 20.