Determine the missing values that would make this equation have infinite amount of solutions. Both answers will be integers. (6 points) 2(5x+6)+2=-6x+_x+_

1 answer

To have an infinite amount of solutions, the missing values must make the equation true regardless of the value of x.

Starting with the equation:
2(5x+6)+2=-6x+_x+_

Distributing the 2 on the left side:
10x + 12 + 2 = -6x + _x + _

Simplifying the equation:
10x + 14 = -6x + _x + _

Combining like terms:
16x + 14 = _x + _

To have an infinite amount of solutions, the coefficients of x on both sides must be equal. Therefore, we can set 16x = _x.

Solving for x:
16x = _x
16 = _

So, the missing values are 16 and 16.
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