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

Answer 1

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

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

To simplify the left side, we can distribute the 8/9 to the terms inside the parentheses:

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

This simplifies to:

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

Next, we can subtract 4/9 from both sides to isolate the (8/9)x term:

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

To subtract the fractions on the right side, we need to find a common denominator:

The common denominator of 3 and 9 is 9, so we can rewrite the expression as:

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

This becomes:

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

Now we can subtract these fractions:

(8/9)x = 92/9

Finally, to solve for x, we can multiply both sides by the reciprocal of (8/9):

x = (92/9)(9/8)

Multiplying the fractions:

x = 828/72

This can be simplified as:

x = 69/6

So the solution to the equation 8/9(x+1/2) = 32/3 is x = 69/6.