Question

Select all the equations that have no solutions. Responses 4 – 6x = 4 4 – 6 x = 4 3x = (x + 9) + 2x 3 x = ( x + 9) + 2 x 6(x – 2) + 4 = 6x – 4 6( x – 2) + 4 = 6 x – 4 7x + 2 = 7x 7 x + 2 = 7 x 7x + 2x – 4 = –8 + 3(3x + 2)

Answer 1

Answer: 4 – 6x = 4 and 7x + 2 = 7x

Explanation:

The equations with no solutions are 4 – 6x = 4 and 7x + 2 = 7x.

The equation 4 – 6x = 4 has no solution because no matter what value is assigned to x, the equation will never be true. The left side of the equation (4 – 6x) will always be a negative number and the right side (4) will always be a positive number, so the equation cannot be satisfied.

The equation 7x + 2 = 7x has no solution because the two sides of the equation are identical. The left side (7x + 2) is equal to the right side (7x). Therefore, no matter what value is assigned to x, the equation will always be true and there is no solution.

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