To solve the equation 8/9(x+1/2)=32/3, follow the steps below:
1. Distribute the 8/9 to the terms inside the parentheses:
(8/9)(x) + (8/9)(1/2) = 32/3
Simplify: 8/9(x) + 4/9 = 32/3
2. Clear the fractions by multiplying all terms by the least common denominator (9) to eliminate the denominators:
9 * (8/9)(x) + 9 * (4/9) = 9 * (32/3)
Simplify: 8x + 4 = 96/3
3. Simplify the right side:
8x + 4 = 32
4. Subtract 4 from both sides of the equation to isolate the variable:
8x + 4 - 4 = 32 - 4
Simplify: 8x = 28
5. Divide both sides by 8 to solve for x:
(8x)/8 = 28/8
Simplify: x = 7/2 or x = 3.5
Therefore, the solution to the equation 8/9(x+1/2)=32/3 is x = 7/2 or x = 3.5.
8/9(x+1/2)=32/3
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