Question

What is the solution of the equation 8/9(x+1/2)=32/3 when solving for x ?(1

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for x in the equation 8/9(x+1/2) = 32/3, we can start by multiplying both sides of the equation by the reciprocal of 8/9, which is 9/8. This will cancel out the fraction on the left side and give us:

(9/8)(8/9)(x+1/2) = (9/8)(32/3)

Simplifying this equation gives us:

1(x+1/2) = 36/1

Now we can distribute the 1 on the left side of the equation:

x + 1/2 = 36/1

Multiplying both sides of the equation by 2 to get rid of the fraction gives:

2(x + 1/2) = 2(36/1)

This simplifies to:

2x + 1 = 72

Subtracting 1 from both sides of the equation gives us:

2x = 71

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 71/2

Answer 2

[AI-generated answer — Explain Bot]

To solve for x in the equation 8/9(x+1/2) = 32/3, we can follow these steps:

Step 1: Distribute the 8/9 to the terms inside the parentheses:
(8/9)x + (8/9)(1/2) = 32/3

Step 2: Simplify the expression inside the parentheses:
(8/9)x + 4/9 = 32/3

Step 3: To eliminate the fractions, we can multiply both sides of the equation by the least common denominator (LCD) of 9 and 3, which is 9:
9 * ((8/9)x + 4/9) = 9 * (32/3)

After simplifying, we get:
8x + 4 = 96

Step 4: To isolate the x-term, subtract 4 from both sides of the equation:
8x + 4 - 4 = 96 - 4
8x = 92

Step 5: Divide both sides of the equation by 8 to solve for x:
(8x)/8 = 92/8
x = 11.5

Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x is x = 11.5.

Answer 3

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

Step 1: Distribute the 8/9 on the left side of the equation.

(8/9) * (x + 1/2) = 32/3

Step 2: Multiply each term inside the parentheses by 8/9.

(8/9)x + (8/9)*(1/2) = 32/3

Step 3: Simplify the equation.

(8/9)x + 4/9 = 32/3

Step 4: To eliminate the fractions, multiply the entire equation by the least common multiple (LCM) of the denominators, which in this case is 9.

9 * [(8/9)x + 4/9] = 9 * (32/3)

Step 5: Simplify both sides of the equation.

8x + 4 = 96/3

8x + 4 = 32

Step 6: Subtract 4 from both sides of the equation.

8x + 4 - 4 = 32 - 4

8x = 28

Step 7: Divide both sides of the equation by 8 to solve for x.

(8x)/8 = 28/8

x = 28/8

Step 8: Simplify the fraction, if necessary.

x = 7/2 or x = 3.5

Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x is x = 7/2 or x = 3.5.