4x + 5x + 12 = -6 (given)
9x + 12 = -6 (simplify)
9x = -18 (subtraction)
x = -2 (addition)
Which reason is incorrect?
The given statement, "4x + 5x + 12 = -6," is incorrect. The correct expression should be "4x + 5x + 12 = -6x."
Justify Solution Steps
To justify the solution steps:
1. Given: The equation provided is 4x + 5x + 12 = -6.
2. Combine like terms: To simplify the equation, add the coefficients of the x terms. 4x + 5x can be combined to give 9x.
3. Add the constant terms: In the equation 9x + 12 = -6, combine the constants on both sides. Adding 12 to both sides gives 9x + 12 = -6.
4. Isolate the variable: To isolate the variable x, subtract 12 from both sides of the equation. This gives 9x = -18.
5. Solve for x: Divide both sides of the equation by 9 to solve for x. This gives x = -2.
Therefore, the solution steps are justified.
The incorrect reason is "subtraction". The correct reason should be "combining like terms".
To determine which reason is incorrect, we need to review the steps that were used to solve the equation.
The given equation is 4x + 5x + 12 = -6.
The first step is to combine the like terms on the left side of the equation. Adding 4x and 5x gives us 9x, so the equation becomes 9x + 12 = -6.
The next step is to simplify the equation by subtracting 12 from both sides. This gives us 9x = -6 - 12, which simplifies to 9x = -18.
Finally, to solve for x, we divide both sides of the equation by 9. By doing so, we get x = -18/9, which simplifies to x = -2.
Looking at the steps, we can see that each step is correct and consistent with the rules of algebra. Therefore, there is no reason that appears to be incorrect. However, it's possible that there may be an error in the way the question was asked or in the presentation of the steps.