Select the correct answer.
Which equation, when solved, gives 8 for the value of x?
A. 5/2x + 7/2 = 3/4x + 14
B. 5/4x - 9 = 3/2x - 12
C. 5/4 x - 2 = 3/2 x - 4
D. 5/2 x - 7 = 3/4x + 14
C. 5/4 x - 2 = 3/2 x - 4
To find the correct equation that gives 8 for the value of x, let's solve each of the given equations step-by-step:
A. 5/2x + 7/2 = 3/4x + 14
To solve this equation, we need to eliminate the fractions. Multiply every term by 4 to get rid of the denominators:
4 * (5/2x + 7/2) = 4 * (3/4x + 14)
10x + 14 = 3x + 56
Next, isolate the x term by subtracting 3x from both sides:
10x - 3x + 14 = 56
7x + 14 = 56
Subtract 14 from both sides to isolate the x term:
7x + 14 - 14 = 56 - 14
7x = 42
Finally, divide both sides by 7 to solve for x:
(7x)/7 = 42/7
x = 6
So, for equation A, x = 6, not 8.
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B. 5/4x - 9 = 3/2x - 12
To solve this equation, let's eliminate the fractions by multiplying every term by 4:
4 * (5/4x - 9) = 4 * (3/2x - 12)
5x - 36 = 6x - 48
Next, isolate the x term by subtracting 5x from both sides:
5x - 5x - 36 = 6x - 5x - 48
-36 = x - 48
Now, let's isolate the x term by adding 48 to both sides:
-36 + 48 = x - 48 + 48
12 = x
So, for equation B, x = 12, not 8.
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C. 5/4 x - 2 = 3/2 x - 4
To solve this equation, let's eliminate the fractions by multiplying every term by 4:
4 * (5/4 x - 2) = 4 * (3/2 x - 4)
5x - 8 = 6x - 16
Next, isolate the x term by subtracting 5x from both sides:
5x - 5x - 8 = 6x - 5x - 16
-8 = x - 16
Now, let's isolate the x term by adding 16 to both sides:
-8 + 16 = x - 16 + 16
8 = x
So, for equation C, x = 8.
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D. 5/2 x - 7 = 3/4x + 14
To solve this equation, let's eliminate the fractions by multiplying every term by 4:
4 * (5/2 x - 7) = 4 * (3/4x + 14)
10x - 28 = 3x + 56
Next, isolate the x term by subtracting 3x from both sides:
10x - 3x - 28 = 3x - 3x + 56
7x - 28 = 56
Now, let's isolate the x term by adding 28 to both sides:
7x - 28 + 28 = 56 + 28
7x = 84
Finally, divide both sides by 7 to solve for x:
(7x)/7 = 84/7
x = 12
So, for equation D, x = 12, not 8.
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Based on our calculations, the correct equation that gives 8 for the value of x is C. 5/4 x - 2 = 3/2 x - 4.