Final answer:
To solve the equation 7(x+3) = 5x - 3, distribute the 7, move variables to one side, constants to the other, combine like terms, and divide to isolate x, which in this case gives x = -12. Always verify by checking the solution in the original equation.
Step-by-step explanation:
Content loaded, Zion is trying to solve the equation 7(x+3) = 5x - 3. To solve for the variable x, follow these steps:
- Distribute the 7 into the parentheses: 7x + 21 = 5x - 3.
- Eliminate terms by moving all x terms to one side and constants to the other side: 7x - 5x = -3 - 21.
- Combine like terms: 2x = -24.
- Divide both sides by 2 to isolate x: x = -12.
- Check the answer by plugging x into the original equation to verify the solution is reasonable: 7(-12 + 3) = 5(-12) - 3 simplifies to -84 = -63, which means there was a mistake. Recheck steps 2 to 4.
- Correct the check step: 7(-12 + 3) = 5(-12) - 3, which simplifies correctly to -63 = -63. The check confirms that x = -12 is a reasonable solution to the equation.