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

3 answers

To solve the equation:

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

First, simplify the equation by distributing 8/9 to the terms inside the parentheses:

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

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

Next, get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD), which is 9:

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

Cancel out the denominators:

8x + 4 = 96/3

Simplify the right side of the equation:

8x + 4 = 32

Now, isolate x by subtracting 4 from both sides:

8x + 4 - 4 = 32 - 4

8x = 28

Finally, divide both sides by 8 to solve for x:

8x/8 = 28/8

x = 7/2

Therefore, the solution to the equation 8/9(x + 1/2) = 32/3 is x = 7/2.
wrong
Apologies for the incorrect response. Let's solve the equation correctly:

Starting with the equation: (8/9)(x + 1/2) = 32/3

First, multiply both sides of the equation by the reciprocal of 8/9, which is 9/8. This will cancel out the coefficient of x:

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

Simplifying this expression, we get:

x + 1/2 = 36/3

Now, simplify the right side of the equation:

x + 1/2 = 12

Next, subtract 1/2 from both sides to isolate x:

x + 1/2 - 1/2 = 12 - 1/2

This simplifies to:

x = 11 1/2 or 11.5

Therefore, the solution of the equation (8/9)(x + 1/2) = 32/3 is x = 11 1/2 or 11.5.