How many solutions does this equation have?
-16u – 12 = 4(-4u – 3)
no solution
one solution
infinitely many solutions
How many solutions does this equation have? -16u – 12 = 4(-4u – 3)
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To determine how many solutions the equation has, let’s solve it step-by-step.
1. Start with the given equation:
[-16u – 12 = 4(-4u – 3)]
2. Distribute the right side:
[-16u – 12 = -16u – 12]
3. Now, simplify the equation:
Move all terms to one side:
[-16u + 16u – 12 + 12 = 0]
This simplifies to:
[0 = 0]
Since the equation simplifies to a statement that is always true (0 = 0), this means that there are infinitely many solutions.
Answer: Infinitely many solutions.
This is because the original equation is an identity that is true for all values of ( u ).