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 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.
To solve the equation 8/9(x + 1/2) = 32/3 for x, we need to isolate the variable x on one side of the equation.
First, let's multiply both sides of the equation by the reciprocal of the coefficient of x, which in this case is 9/8.
(9/8) * (8/9)(x + 1/2) = (9/8) * (32/3)
On the left side, the 8/9 cancels out with the 9/8, leaving us with:
(x + 1/2) = (32/3)
Next, let's simplify the right side of the equation:
32/3 = (10 + 2/3)
Now we have:
(x + 1/2) = (10 + 2/3)
To eliminate the fraction on the right side, we'll need to find a common denominator. The least common multiple of 2 and 3 is 6. So, let's rewrite the equation:
(x + 1/2) = (10 + 4/6)
Now, let's convert the fractions on the right side to have the same denominator:
(x + 1/2) = (10 + 8/6)
Next, let's combine the fractions on the right side:
(x + 1/2) = (10 + 4/3)
We have now simplified the equation to:
(x + 1/2) = (34/3)
To isolate x, we'll subtract 1/2 from both sides:
x = (34/3) - (1/2)
To add or subtract fractions, we need a common denominator, which in this case is 6. Therefore, we'll rewrite the equation as follows:
x = (34/3) * (2/2) - (1/2) * (3/3)
Simplifying further, we have:
x = (68/6) - (3/6)
Now, we can subtract the fractions:
x = (68 - 3)/6
Finally, we arrive at the solution:
x = 65/6