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

Answer 1

To solve the equation 8/9(x+1/2) = 32/3 for x as a fraction, we can follow the steps below:

First, let's simplify the equation by multiplying both sides by the reciprocal of 8/9, which is 9/8:
(8/9(x+1/2)) * (9/8) = (32/3) * (9/8)
(x+1/2) = 36/1

Next, let's isolate the x term by subtracting 1/2 from both sides of the equation:
(x + 1/2) - 1/2 = 36/1 - 1/2
x = 36/1 - 1/2

To subtract 1/2 from 36/1, we need to have a common denominator. The common denominator is 2, so we can convert 36/1 to the fraction 72/2:
x = 72/2 - 1/2

Now that the fractions have the same denominator, we can combine them:
x = (72 - 1)/2
x = 71/2

Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x as a fraction is x = 71/2.

Answer 2

that is not correct

Answer 3

Apologies for the mistake. Let's solve the equation correctly:

To solve the equation 8/9(x+1/2) = 32/3 for x as a fraction, let's begin by distributing the 8/9 to the terms inside the parentheses:

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

Now, let's simplify both sides by canceling out common factors:

(8/9)*(x+1/2) = 32/3
(8/9)*x + (8/9)*(1/2) = 32/3
(8/9)*x + 4/9 = 32/3

Next, let's get rid of the fraction by multiplying both sides of the equation by the reciprocal of 4/9, which is 9/4:

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

Simplifying further:

x + 1 = (3/4)*(32/1)
x + 1 = 96/4
x + 1 = 24

Now, let's isolate x by subtracting 1 from both sides of the equation:

x + 1 - 1 = 24 - 1
x = 23

Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x as a fraction is x = 23.

Answer 4

still wrong

Answer 5

Apologies for the previous incorrect response. Let's solve the equation correctly this time:

To solve the equation 8/9(x+1/2) = 32/3 for x as a fraction, let's begin by simplifying both sides of the equation:

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

We can simplify the left side by multiplying 8/9 by x and 8/9 by 1/2:

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

Now, let's multiply the fractions:

(8/9)x + 4/18 = 32/3

Simplify further:

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

To eliminate the fractions, let's multiply both sides of the equation by the reciprocal of 2/9, which is 9/2:

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

Multiplying the fractions:

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

Simplify:

x + 1 = 144/6

Now, subtract 1 from both sides of the equation:

x + 1 - 1 = 144/6 - 1
x = 144/6 - 6/6
x = (144 - 6)/6
x = 138/6

Simplify the fraction:

x = 23/1

Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x as a fraction is x = 23/1.