What is the solution of the equation 8/9(x+1/2)=32/3 when solving for x?
To solve the equation 8/9(x+1/2) = 32/3 for x, we can begin by simplifying both sides of the equation.
Firstly, let's simplify the left side of the equation:
8/9(x + 1/2) = (8/9) * x + (8/9) * (1/2) = (8/9)x + 4/9
Now we have the equation:
(8/9)x + 4/9 = 32/3
Next, we can get rid of the fraction by multiplying every term in the equation by 9, to cancel out the denominators:
9 * ((8/9)x + 4/9) = 9 * (32/3)
8x + 4 = 96/3
Simplifying the right side:
8x + 4 = 32
To isolate the variable, we can subtract 4 from both sides of the equation:
8x + 4 - 4 = 32 - 4
8x = 28
Finally, to solve for x, we divide both sides by 8:
(8x)/8 = 28/8
x = 7/2
Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x is x = 7/2.
To solve the equation 8/9(x + 1/2) = 32/3 for x, we can follow these steps:
Step 1: Distribute the 8/9 to the terms inside the parentheses.
(8/9)(x + 1/2) = 32/3
(8/9)(x) + (8/9)(1/2) = 32/3
8/9x + 4/9 = 32/3
Step 2: Simplify the equation by combining like terms.
8/9x + 4/9 = 32/3
Step 3: To eliminate the fractions, multiply both sides of the equation by the least common denominator (9 * 3 = 27).
27 * (8/9x + 4/9) = 27 * (32/3)
(27 * 8/9x) + (27 * 4/9) = 27 * 32/3
(216/9x) + (108/9) = 864/3
Step 4: Simplify further by canceling out the denominators.
24x + 12 = 288
Step 5: Subtract 12 from both sides of the equation.
24x + 12 - 12 = 288 - 12
24x = 276
Step 6: Divide both sides of the equation by 24 to solve for x.
x = 276/24
Step 7: Simplify the right side of the equation.
x = 11 1/2
Therefore, the solution to the equation 8/9(x + 1/2) = 32/3 is x = 11 1/2.
To solve the equation (8/9)(x + 1/2) = 32/3 for x, follow these steps:
Step 1: Simplify both sides of the equation
Multiply each term inside the parentheses by 8/9:
(8/9)(x + 1/2) = 32/3
(8/9)(x) + (8/9)(1/2) = 32/3
(8/9)(x) + (4/9) = 32/3
Step 2: Combine like terms
Add (4/9) to both sides of the equation:
(8/9)(x) + (4/9) + (4/9) = 32/3 + (4/9)
(8/9)(x) + (8/9) = 32/3 + (4/9)
(8/9)(x) + (8/9) = 32/3 + (4/9)
Step 3: Simplify the right side of the equation
To add 32/3 and 4/9, you need to find a common denominator. The least common multiple of 3 and 9 is 9:
32/3 + 4/9 = (32/3)(3/3) + (4/9)(1/1)
= 96/9 + 4/9
= 100/9
So, the equation becomes:
(8/9)(x) + (8/9) = 100/9
Step 4: Isolate the x-term
Subtract (8/9) from both sides of the equation:
(8/9)(x) + (8/9) - (8/9) = 100/9 - (8/9)
(8/9)(x) = 100/9 - (8/9)
(8/9)(x) = 92/9
Step 5: Solve for x
To solve for x, multiply both sides of the equation by the reciprocal of (8/9):
(8/9)(x) * (9/8) = (92/9) * (9/8)
x = (92/9) * (9/8)
Now, we can simplify:
x = 92/8
x = 11.5
Therefore, the solution to the equation (8/9)(x + 1/2) = 32/3 when solving for x is x = 11.5.