what is the sum of the solutions of the equation
|2x-7|=11?
A) -9
B) -7
C) 5
D) 7
E) 9
***What is the most efficient way to solve this?
another way
not good way to silve this
To find the sum of the solutions of the equation |2x-7|=11, we need to solve it first.
The most efficient way to solve this equation is to split it into two separate equations and solve each one.
First, let's solve 2x-7=11 by adding 7 to both sides, and we get 2x=18. Then, divide both sides by 2, giving us x=9.
Next, let's solve -(2x-7)=11 by first distributing the negative sign, which gives us -2x+7=11. Subtracting 7 from both sides, we have -2x=4. Dividing both sides by -2, we get x=-2.
Thus, the solutions to the original equation are x=9 and x=-2.
To find the sum of the solutions, we add them together: 9 + (-2) = 7.
Therefore, the sum of the solutions of the equation |2x-7|=11 is 7. Therefore, the correct answer choice is option D) 7.
|2x-7|=11
2x-7 = 11 OR -2x+7 = 11
2x = 18 OR -2x = 4
x = 9 OR x = -2
so the sum of the solutions is 9-2 = 7