when the opposite of twice the price of an item is added to 10, the result is the same as half of the…

when the opposite of twice the price of an item is added to 10, the result is the same as half of the opposite of the sum of the price and 7. what is the price of the item?\na) -\\frac{14}{3}\nb) 2\nc) 4.33\nd) 9

when the opposite of twice the price of an item is added to 10, the result is the same as half of the opposite of the sum of the price and 7. what is the price of the item?\na) -\\frac{14}{3}\nb) 2\nc) 4.33\nd) 9

Answer

Explanation:

Step1: Let the price be $x$.

The opposite of twice the price is $- 2x$. Adding it to 10 gives $10-2x$. The sum of the price and 7 is $x + 7$, and the opposite of it is $-(x + 7)$. Half of this is $\frac{-(x + 7)}{2}$. So the equation is $10-2x=\frac{-(x + 7)}{2}$.

Step2: Multiply both sides by 2 to clear the fraction.

$2(10 - 2x)=-(x + 7)$. Expanding gives $20-4x=-x - 7$.

Step3: Add $4x$ to both sides.

$20=-x - 7+4x$, which simplifies to $20 = 3x-7$.

Step4: Add 7 to both sides.

$20 + 7=3x$, so $27 = 3x$.

Step5: Divide both sides by 3.

$x = 9$.

Answer:

D. 9