Final answer:
To solve the equation 4(x + 2) = 2x, distribute the 4, eliminate terms, and isolate x to find x = -4. Checking the solution by substituting -4 into the original equation confirms that x = -4 is correct.
Step-by-step explanation:
To check if the solution works for the equation 4(x + 2) = 2x algebraically, let us solve the equation step-by-step:
- Start by distributing the 4 into the parentheses: 4x + 8 = 2x.
- Subtract 2x from both sides to eliminate the x-term on the right side of the equation: 4x - 2x + 8 = 2x - 2x, which simplifies to 2x + 8 = 0.
- Now, subtract 8 from both sides to isolate the x-term: 2x + 8 - 8 = 0 - 8, which simplifies to 2x = -8.
- Finally, divide both sides by 2 to solve for x: 2x/2 = -8/2, resulting in x = -4.
To check if this is the correct solution, substitute x with -4 back into the original equation:
- 4(-4 + 2) = 2(-4)
- 4(-2) = -8
- -8 = -8
Since both sides equal -8, the solution x = -4 is correct.
When working on such problems, it's essential to eliminate terms wherever possible to simplify the algebra and to check the answer to see if it is reasonable. Multiplication or division by the same number does not change equality, and it is very important to apply it correctly to maintain the integrity of the equation.