What is the solution of the equation 8/9(x+1/2)=32/3 when solving for x ?(1 point)
To solve the equation:
8/9(x+1/2) = 32/3
First, distribute the 8/9 to the terms inside the parentheses:
(8/9)(x) + (8/9)(1/2) = 32/3
Simplify the right side:
(8/9)(x) + 4/9 = 32/3
To eliminate a fraction, multiply both sides of the equation by 9:
(9)((8/9)(x) + 4/9) = (9)(32/3)
Simplify both sides:
8x + 4 = 96/3
Multiply on the right side:
8x + 4 = 32
Subtract 4 from both sides:
8x = 32 - 4 = 28
Divide both sides by 8:
(8x)/8 = 28/8
Simplify:
x = 3.5
To solve the equation:
8/9(x+1/2) = 32/3
We will begin by simplifying both sides of the equation.
Step 1: Distribute 8/9 to the expressions inside the parentheses.
8/9 * x + 8/9 * 1/2 = 32/3
Step 2: Simplify the right side of the equation.
8/9 * x + 4/9 = 32/3
Step 3: Multiply both sides by the reciprocal of 8/9 (which is 9/8) to isolate the x term.
(9/8)(8/9 * x + 4/9) = (9/8)(32/3)
Step 4: Simplify both sides of the equation.
x + 9/2 = 36/1
Step 5: Subtract 9/2 from both sides of the equation.
x + 9/2 - 9/2 = 36/1 - 9/2
x = 36/1 - 9/2
Step 6: Combine the fractions on the right side of the equation.
x = 36/1 - 18/2
x = 36/1 - 9
Step 7: Simplify the right side of the equation.
x = 36 - 9
x = 27
Therefore, the solution to the equation 8/9(x+1/2) = 32/3 is x = 27.