What is the solution to 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, you can follow these steps:

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

2. Simplify the expression by multiplying each term by their respective denominators:
8/9 * x + 8/9 * 1/2 = 32/3

This simplifies to:
8/9 * x + 4/9 = 32/3

3. Multiply both sides of the equation by the reciprocal of the coefficient of x to isolate x. In this case, the reciprocal of 8/9 is 9/8, so we have:
(9/8) * (8/9) * x + (9/8) * (4/9) = x + (9/8) * (32/3)

This simplifies to:
1x + 4/2 = x + 12/3

1x + 2 = x + 4

4. Subtract x from both sides of the equation:
1x - x + 2 = x - x + 4

This simplifies to:
0x + 2 = 4

5. Subtract 2 from both sides of the equation:
0x + 2 - 2 = 4 - 2

This simplifies to:
0 = 2

Since the equation leads to a contradiction (0 ≠ 2), it shows that there is no solution to this equation.