Which of these equations has no solutions? Choices: (A)4(x + 3) = 4(x - 3) (B)3x + x - 3 = 1/3(12x - 9) (C)2x + 3 - 4x = 4x + 3 Which statement explains a way you can tell the equation has no solutions? Choices: (A)It is equivalent to an equation that has the same variable terms but different constant terms on each side of the equal sign. (B)It is equivalent to an equation that has the same variable terms and the same constant terms on each side of the equal sign. (C)It is equivalent to an equation that has different variable terms on each side of the equation.

Question

Which of these equations has no solutions?   Choices: (A)4(x + 3) = 4(x - 3) (B)3x + x - 3 = 1/3(12x - 9) (C)2x + 3 - 4x = 4x + 3    Which statement explains a way you can tell the equation has no solutions?   Choices: (A)It is equivalent to an equation that has the same variable terms but different constant terms on each side of the equal sign. (B)It is equivalent to an equation that has the same variable terms and the same constant terms on each side of the equal sign. (C)It is equivalent to an equation that has different variable terms on each side of the equation.

Bytelearn · Accepted Answer

Distribute and Simplify:  Simplify equation (A) 4(x + 3) = 4(x - 3). Distribute the 4 on both sides: 4x + 12 = 4x - 12. Subtract 4x from both sides: 12 = -12. No Solution for Equation (A):  Since 12 does not equal -12, equation (A) simplifies to a false statement, indicating no solutions. Combine and Distribute:  Simplify equation (B) 3x + x - 3 = 1/3(12x - 9). Combine like terms on the left: 4x - 3. Distribute the 1/3 on the right: 4x - 3. Both sides are equal, suggesting infinite solutions. Solve for x in Equation (C):  Simplify equation (C) 2x + 3 - 4x = 4x + 3. Combine like terms on the left: -2x + 3. The equation becomes -2x + 3 = 4x + 3. Subtract 3 from both sides: -2x = 4x. Add 2x to both sides: 0 = 6x. Divide by 6: x = 0. This equation has a solution.

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