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
First, multiply both sides of the equation by 9 to eliminate the fraction on the left side:
9 * 8/9(x+1/2) = 9 * 32/3
8(x + 1/2) = 96/3
Multiplying 9/9 by (x + 1/2) on the left side:
8(x + 1/2) = 32
Now, distribute 8 to the terms inside the parentheses:
8x + 4 = 32
Then, subtract 4 from both sides of the equation:
8x + 4 - 4 = 32 - 4
8x = 28
Finally, divide both sides of the equation by 8:
(8x)/8 = 28/8
x = 7/2
Therefore, the solution to the equation is x = 7/2.
this is wrong
Apologies for the mistake. Let's rework the solution correctly:
To solve the equation:
8/9(x+1/2) = 32/3
First, let's simplify the equation by multiplying both sides by the reciprocal of 8/9, which is 9/8:
(9/8) * 8/9(x + 1/2) = (9/8) * 32/3
This simplifies to:
x + 1/2 = (9/8) * 32/3
Next, let's simplify the right side:
x + 1/2 = 36/1
To eliminate the fraction on the left side, we need to find a common denominator:
x + 1/2 = 36/1
To convert 1/2 to twelfths, we multiply the numerator (1) and denominator (2) by 6:
x + 6/12 = 36/1
Now the left side has a common denominator of 12:
x + 6/12 = 36/1
Next, let's convert the whole number 36 to twelfths:
x + 6/12 = 36/1 * 12/12
This simplifies to:
x + 6/12 = 432/12
Now, the equation becomes:
x + 6/12 = 432/12
To isolate x, let's subtract 6/12 from both sides:
x + 6/12 - 6/12 = 432/12 - 6/12
This simplifies to:
x = 426/12
Lastly, we can simplify the fraction:
x = 71/2
Therefore, the solution to the equation is x = 71/2.
wrong
Apologies for the mistake in my previous response. Let's rework the solution correctly:
To solve the equation:
8/9(x+1/2) = 32/3
First, let's distribute the 8/9 to the terms inside the parentheses:
(8/9) * (x + 1/2) = 32/3
This simplifies to:
(8/9) * x + (8/9) * (1/2) = 32/3
Multiplying the fractions:
(8/9) * x + 8/18 = 32/3
Simplifying the fractions:
(8/9) * x + 4/9 = 32/3
To eliminate the fractions, let's multiply both sides of the equation by 9:
9 * ((8/9) * x + 4/9) = 9 * (32/3)
This simplifies to:
8x + 4 = 96/3
We can simplify 96/3 as well:
8x + 4 = 32
Now, subtract 4 from both sides of the equation:
8x + 4 - 4 = 32 - 4
This simplifies to:
8x = 28
Lastly, divide both sides of the equation by 8 to solve for x:
(8x)/8 = 28/8
This simplifies to:
x = 7/2
Therefore, the solution to the equation is x = 7/2. Apologies for the confusion in my initial responses.
7/2 is wrong
Apologies for the continued confusion. Let's rework the solution correctly:
To solve the equation:
8/9(x + 1/2) = 32/3
First, let's simplify the equation by multiplying both sides by the reciprocal of 8/9, which is 9/8:
(9/8) * (8/9)(x + 1/2) = (9/8) * (32/3)
This simplifies to:
x + 1/2 = (9/8) * (32/3)
Next, let's simplify the right side:
x + 1/2 = (36/8) * (32/3)
To multiply the fractions, we can first simplify 36/8 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4:
x + 1/2 = (9/2) * (32/3)
Now, multiply the numerators and denominators:
x + 1/2 = (9 * 32)/(2 * 3)
This simplifies to:
x + 1/2 = 288/6
Further simplifying the right side:
x + 1/2 = 48/1
To convert 1/2 to twelfths, we multiply the numerator (1) and denominator (2) by 6:
x + 6/12 = 48/1
Now the left side has a common denominator of 12:
x + 6/12 = 48/1
Next, let's convert the whole number 48 to twelfths:
x + 6/12 = 48/1 * 12/12
This simplifies to:
x + 6/12 = 576/12
Now, subtract 6/12 from both sides:
x + 6/12 - 6/12 = 576/12 - 6/12
This simplifies to:
x = 570/12
Lastly, we can simplify the fraction:
x = 95/2
Therefore, the solution to the equation is x = 95/2. I apologize for the confusion in my previous responses.
95/2 is wrong
Apologies for the earlier mistakes. Let's rework the solution correctly:
To solve the equation:
8/9(x+1/2) = 32/3
First, let's simplify the equation by multiplying both sides by 9/8 (the reciprocal of 8/9):
(9/8)*[8/9(x+1/2)] = (9/8)*(32/3)
On the left side, the 8/9 and 9/8 cancel out, leaving us with:
x + 1/2 = (9/8)*(32/3)
Now, let's simplify the right side:
x + 1/2 = 288/24
Next, let's simplify the fraction on the right side by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 24:
x + 1/2 = 12/1
To convert 1/2 to a common denominator of 2, we multiply the numerator (1) by 2:
x + 2/4 = 12/1
Now, let's convert the whole number 12 to a fraction with a denominator of 4:
x + 2/4 = 48/4
Now, we have a common denominator of 4:
x + 2/4 = 48/4
To isolate x, subtract 2/4 from both sides:
x + 2/4 - 2/4 = 48/4 - 2/4
This simplifies to:
x = 46/4
Finally, 46/4 can be simplified as follows:
x = 23/2
Therefore, the solution to the equation is x = 23/2.