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Answer :
Final answer:
In summary, only Choice C has infinitely many solutions, because it forms an identity (something that is always true no matter the value of the variable 'x').
Explanation:
The question asks which of the following equations have infinitely many solutions. The answer depends on whether or not the left and right-hand sides of each equation are identical. To determine this, we must simplify each equation.
- Choice A: simplifying the typo-filled equation, we can see that it effectively forms a contradiction where something is made equal to something else that's different. Hence, this equation does not have infinitely many solutions.
- Choice B: the typo made this equation hard to interpret accurately, but it comes very similar to the A choice situation which means it also may not have infinitely many solutions.
- Choice C: Again ignoring the typo, we see the equation is -76x + 76 = -76x + 76, which is always true regardless of the value of 'x'. Therefore, this equation has infinitely many solutions.
- Choice D: This reads as -76x + 76 = 76x + 76, which will only be true if 'x' equals 0. Therefore, this equation does not have infinitely many solutions.
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