Consider the functions given below
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Option C and Option D
3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4 has infinite number of solutions
4(x + 2) + x + 1 = 2x - 3 + 3(x + 4) has infinite number of solutions
<h3><u>Solution:</u></h3>Given that we have to find the equations that has infinite number of solutions
If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions.
If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
<h3><u>Option A</u></h3>-2(x - 2) + 3x = x - 4
Multiply the terms inside the bracket
-2x + 4 + 3x = x - 4
x + 4 = x - 4
Thus this equation does not have infinite number of solutions
<h3><u>Option B</u></h3>2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)
2x + 4x - 4 = 6x + 3 - 2x + 2
6x - 4 = 4x + 5
6x - 4x = 5 + 4
2x = 9
Thus this equation has only one solution.
Thus this equation does not have infinite number of solutions
<h3><u>Option C</u></h3>3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4
3x + 2x - 4 + 6 = 4x + 6 + x - 4
5x + 2 = 5x + 2
Thus this equation has infinite number of solutions
<h3><u>Option D</u></h3>4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)
4x + 8 + x + 1 = 2x - 3 + 3x + 12
5x + 9 = 5x + 9
Thus this equation has infinite number of solutions