Select the correct answer.
What is the solution of 5/2x - 7 = 3/4x + 14?
?
A. x = -6
B. x = 6
C. x = 8
D. x = 12
AAAaannndd the bot gets it wrong yet again!
does x=6 work?
5/2 (6) - 7 = 15-7 = 8
3/4 (6) + 14 = 189.5
so, NO
5/2 x - 7 = 3/4 x + 14
7/4 x = 21
x = 12
My apologies for the mistake. You are correct, the solution is x = 12. Thank you for providing the correct explanation.
To find the solution of the equation (5/2)x - 7 = (3/4)x + 14, we need to isolate the variable x.
1. Start by simplifying both sides of the equation:
5/2x - 7 = 3/4x + 14
2. To get rid of the fraction on the left side, multiply every term by 2:
2 * (5/2x) - 2 * 7 = 2 * (3/4x) + 2 * 14
5x - 14 = (6/4)x + 28
3. Simplify further:
5x - 14 = (3/2)x + 28
4. To get rid of the fraction on the right side, multiply every term by 2:
2 * (5x - 14) = 2 * ((3/2)x + 28)
10x - 28 = 3x + 56
5. Move the terms with x to one side of the equation and the constants to the other side:
10x - 3x = 56 + 28
7x = 84
6. Divide both sides of the equation by 7 to solve for x:
x = 84/7
7. Simplify the fraction:
x = 12
Therefore, the correct answer is D. x = 12.
To find the solution to the equation 5/2x - 7 = 3/4x + 14, we need to isolate the variable x on one side of the equation. Here's how you can do it:
1. Start by getting rid of the fractions by multiplying every term in the equation by the least common denominator (LCD) of 2 and 4, which is 4. Multiplying each term by 4, we get:
4 * (5/2x) - 4 * 7 = 4 * (3/4x) + 4 * 14
Simplifying, we have:
10x - 28 = 3x + 56
2. Next, gather like terms on each side of the equation. In this case, combine the x terms on the right side and the constant terms on the left side:
10x - 3x = 56 + 28
Simplifying further:
7x = 84
3. Finally, solve for x by dividing both sides of the equation by 7:
x = 84 / 7
Simplifying the expression:
x = 12
Therefore, the correct answer is D. x = 12.