To solve the equation 8/9 (x + 1/2) = 32/3, we can begin by simplifying the equation:
8/9 (x + 1/2) = 32/3
8/9 * x + 8/9 * 1/2 = 32/3
8/9 * x + 4/9 = 32/3
Next, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which is 9/8, to isolate x:
(8/9 * x + 4/9) * (9/8) = (32/3) * (9/8)
(8/9 * 9/8) * x + 4/9 * 9/8 = 32/3 * 9/8
x + 4/8 = 288/24
x + 1/2 = 12
Finally, we can subtract 1/2 from both sides to solve for x:
x + 1/2 - 1/2 = 12 - 1/2
x = 11.5
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 11.5.
what is the solution of the equation 8/9 (x+1/2) = 32/3
11 answers
sorry i meant to add when solving for x
No problem! To solve for x, we can begin by simplifying the equation:
8/9 (x + 1/2) = 32/3
Multiply both sides by the reciprocal of 8/9, which is 9/8:
(x + 1/2) * (9/8) = (32/3) * (9/8)
(x + 1/2) * (9/8) = 36/1
(x + 1/2) * (9/8) = 36
Distribute:
9/8 * x + 9/8 * 1/2 = 36
9/8 * x + 9/16 = 36
Multiply through by the common denominator of 16 to eliminate the fractions:
16 * (9/8 * x) + 16 * (9/16) = 16 * 36
18x + 9 = 576
Subtract 9 from both sides:
18x = 567
Divide both sides by 18:
x = 567/18
Simplify the fraction:
x = 31.5
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 31.5.
8/9 (x + 1/2) = 32/3
Multiply both sides by the reciprocal of 8/9, which is 9/8:
(x + 1/2) * (9/8) = (32/3) * (9/8)
(x + 1/2) * (9/8) = 36/1
(x + 1/2) * (9/8) = 36
Distribute:
9/8 * x + 9/8 * 1/2 = 36
9/8 * x + 9/16 = 36
Multiply through by the common denominator of 16 to eliminate the fractions:
16 * (9/8 * x) + 16 * (9/16) = 16 * 36
18x + 9 = 576
Subtract 9 from both sides:
18x = 567
Divide both sides by 18:
x = 567/18
Simplify the fraction:
x = 31.5
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 31.5.
sorry but thats wrong
Apologies for the mistake. Let's solve the equation correctly:
To solve the equation 8/9 (x + 1/2) = 32/3, we can begin by distributing the 8/9 to both terms inside the parentheses:
(8/9) * x + (8/9) * (1/2) = 32/3
Multiplying the fractions:
(8/9) * x + 4/9 = 32/3
Now, we can eliminate the fractions by multiplying both sides of the equation by the common denominator of 9:
9 * [(8/9) * x + 4/9] = 9 * (32/3)
This simplifies to:
8x + 4 = 96/3
Combining like terms on the right side:
8x + 4 = 32
Next, we can subtract 4 from both sides:
8x = 32 - 4
8x = 28
Dividing both sides by 8:
x = 28/8
Simplifying the fraction:
x = 7/2
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 7/2.
To solve the equation 8/9 (x + 1/2) = 32/3, we can begin by distributing the 8/9 to both terms inside the parentheses:
(8/9) * x + (8/9) * (1/2) = 32/3
Multiplying the fractions:
(8/9) * x + 4/9 = 32/3
Now, we can eliminate the fractions by multiplying both sides of the equation by the common denominator of 9:
9 * [(8/9) * x + 4/9] = 9 * (32/3)
This simplifies to:
8x + 4 = 96/3
Combining like terms on the right side:
8x + 4 = 32
Next, we can subtract 4 from both sides:
8x = 32 - 4
8x = 28
Dividing both sides by 8:
x = 28/8
Simplifying the fraction:
x = 7/2
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 7/2.
still wrong
Apologies again for the previous incorrect response.
To solve the equation 8/9 (x + 1/2) = 32/3 correctly, we can begin by distributing the 8/9 to both terms inside the parentheses:
(8/9) * x + (8/9) * (1/2) = 32/3
Multiplying the fractions:
(8/9) * x + 4/9 = 32/3
Now, let's find a common denominator for 9 and 3, which is 9:
(8/9) * x + 4/9 = (32/3) * (3/3)
(8/9) * x + 4/9 = 96/9
Now, the equation becomes:
(8/9) * x + 4/9 = 96/9
To eliminate the denominators, we can multiply both sides by the reciprocal of 9/8, which is 8/9:
[(8/9) * x + 4/9] * (8/9) = (96/9) * (8/9)
[(8/9) * 8/9] * x + (4/9) * 8/9 = 96/81 * 8/9
8/9 * x + 32/81 = 96/81
Now, we can subtract 32/81 from both sides:
8/9 * x + 32/81 - 32/81 = 96/81 - 32/81
8/9 * x = 64/81
To solve for x, we can multiply both sides by the reciprocal of 8/9, which is 9/8:
[(8/9) * x] * (9/8) = (64/81) * (9/8)
[(8/9) * 9/8] * x = 64/81 * 9/8
x = 576/648
Now, simplify the fraction:
x = 9/8
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 9/8.
To solve the equation 8/9 (x + 1/2) = 32/3 correctly, we can begin by distributing the 8/9 to both terms inside the parentheses:
(8/9) * x + (8/9) * (1/2) = 32/3
Multiplying the fractions:
(8/9) * x + 4/9 = 32/3
Now, let's find a common denominator for 9 and 3, which is 9:
(8/9) * x + 4/9 = (32/3) * (3/3)
(8/9) * x + 4/9 = 96/9
Now, the equation becomes:
(8/9) * x + 4/9 = 96/9
To eliminate the denominators, we can multiply both sides by the reciprocal of 9/8, which is 8/9:
[(8/9) * x + 4/9] * (8/9) = (96/9) * (8/9)
[(8/9) * 8/9] * x + (4/9) * 8/9 = 96/81 * 8/9
8/9 * x + 32/81 = 96/81
Now, we can subtract 32/81 from both sides:
8/9 * x + 32/81 - 32/81 = 96/81 - 32/81
8/9 * x = 64/81
To solve for x, we can multiply both sides by the reciprocal of 8/9, which is 9/8:
[(8/9) * x] * (9/8) = (64/81) * (9/8)
[(8/9) * 9/8] * x = 64/81 * 9/8
x = 576/648
Now, simplify the fraction:
x = 9/8
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 9/8.
bro stop trolling i want the real answers not the wrong ones stop trying to make me fail and actually help me
Apologies for any confusion caused. To solve the equation correctly:
To solve the equation 8/9 (x + 1/2) = 32/3, we can begin by distributing the 8/9 to both terms inside the parentheses:
(8/9) * x + (8/9) * (1/2) = 32/3
Multiplying the fractions:
(8/9) * x + 4/18 = 32/3
Simplifying the fractions:
8x/9 + 4/18 = 32/3
To simplify further, we can find the least common denominator (LCD) for the fractions 9 and 18, which is 18:
(8x * 2 + 4) / 18 = 32/3
(16x + 4) / 18 = 32/3
Now, we can cross-multiply to eliminate the fractions:
3 * (16x + 4) = 32 * 18
48x + 12 = 576
Next, subtract 12 from both sides:
48x = 564
Finally, divide both sides by 48 to solve for x:
x = 564/48
Simplify the fraction:
x = 47/4
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 47/4.
To solve the equation 8/9 (x + 1/2) = 32/3, we can begin by distributing the 8/9 to both terms inside the parentheses:
(8/9) * x + (8/9) * (1/2) = 32/3
Multiplying the fractions:
(8/9) * x + 4/18 = 32/3
Simplifying the fractions:
8x/9 + 4/18 = 32/3
To simplify further, we can find the least common denominator (LCD) for the fractions 9 and 18, which is 18:
(8x * 2 + 4) / 18 = 32/3
(16x + 4) / 18 = 32/3
Now, we can cross-multiply to eliminate the fractions:
3 * (16x + 4) = 32 * 18
48x + 12 = 576
Next, subtract 12 from both sides:
48x = 564
Finally, divide both sides by 48 to solve for x:
x = 564/48
Simplify the fraction:
x = 47/4
Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 47/4.
thank you
You're welcome! If you have any more questions, feel free to ask.
2 answers