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

Answer 1

To solve the equation 8/9(x + 1/2) = 32/3 for x, we can begin by simplifying:

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

Next, we distribute the 8/9 to both terms inside the parentheses:

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

Now we can simplify the equation further by multiplying:

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

To get rid of the denominators, we can multiply both sides of the equation by 9:

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

This simplifies to:

8x + 4 = 96/3

8x + 4 = 32

Subtracting 4 from both sides of the equation:

8x = 32 - 4

8x = 28

Finally, divide both sides of the equation by 8:

x = 28/8

x = 7/2

Therefore, the solution to the equation is x = 7/2.

Answer 2

Wrong

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, we can begin by simplifying:

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

Next, we distribute the 8/9 to both terms inside the parentheses:

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

Simplifying further:

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

The denominators on both sides of the equation are 9 and 3, so we need to find a common denominator to combine them:

Multiplying the numerator and denominator of the fraction 32/3 by 3, we get:

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

8x/9 + 4/9 = 96/9

Now, we can combine the fractions on the left side:

(8x + 4)/9 = 96/9

To isolate x, we can multiply both sides of the equation by 9:

9 * (8x + 4)/9 = 9 * 96/9

Simplifying:

8x + 4 = 96

Subtracting 4 from both sides:

8x = 96 - 4

8x = 92

Finally, divide both sides by 8:

x = 92/8

Reducing the fraction:

x = 23/2

Therefore, the solution to the equation is x = 23/2.