Question

What is the reason for each step in the solution of the equation 2x = -4(x-3)? Match the reason with the correct step in the equation.

Answer 1

Solve the equation 2x = -4(x-3) by expanding the right side, combining like terms, and isolating the variable x, leading to the final answer x = 2.

The solution of the equation 2x = -4(x-3) involves several algebraic steps. These steps correspond with the provided information, which is similar to the scientific method for approaching problems.

1. Expand the right side of the equation to eliminate the parentheses: 2x = -4x + 12. This uses the distributive property of multiplication over addition.
2. Move all x terms to one side of the equation: 2x + 4x = 12. This step involves combining like terms.
3. Solve for x by dividing both sides by the coefficient of x: x = 12 / 6. This isolates the variable to find its value.
4. Check the math by substituting the solution back into the original equation to verify it satisfies the equation.

The answer after these steps is x = 2. This value satisfies the original equation, confirming it is correct.