Section: Math 0 Likes
How many solutions does the equation 4(x-2) = -2(x+4) have? (May 2023 U.S.)
How many solutions does the equation 4(x-2) = -2(x+4) have?
A. Zero
B. Exactly one
C. Exactly two
D. Infinitely many
Solution
Correct answer: B. Exactly one.
To solve this problem, we need to simplify the equation and then solve for the value of x.
The given equation is:
4(x-2) = -2(x+4)
Simplifying the equation:
4x - 8 = -2x - 8
6x = 0
x = 0
Now, let's check if there are any other solutions.
Substituting x = 0 back into the original equation:
4(0-2) = -2(0+4)
-8 = -8
The equation is satisfied when x = 0.
Therefore, the equation 4(x-2) = -2(x+4) has exactly one solution, which is x = 0.
Exam Edition: May 2023 U.S.
Exam Year: 2023
Related topics: Solving Linear Equations, Algebraic Manipulation