Question

3(x – 2) + 4x = 10(x + 1)

so I know what the answer is and know how to do it to some extent, my question is, when this simplifies to 3x - 6 + 4x = 10x + 10 when we combine the 10x and 3x, how would you know to subtract or add, I know what the inverse operation rules are, but since there is a + and a -, how would you know which inverse operation to do, adding or subtracting, because as I said there is a + and a - ( I have asked this question to so many people and my question is not comprehended, I am trying to make it as clear as possible, you deserve 100 points for this if you manage to help me understand, I just need someone who comprehends what I am asking).

Answer 1

To simplify the equation 3(x - 2) + 4x = 10(x + 1) and isolate x, one must combine like terms and use inverse operations appropriately: addition becomes subtraction for like terms, and vice versa. By consolidating like terms and then dividing to isolate x, it's revealed that x = -4/3. To ensure accuracy, these steps should be followed carefully and the solution checked by plugging it back into the original equation.

Step-by-step explanation:

When simplifying an equation like 3(x – 2) + 4x = 10(x + 1), we combine like terms on each side. After expanding and combining terms, we get 3x - 6 + 4x = 10x + 10. To isolate the variable x, we need to get all the x terms on one side and the constants on the other. This involves inverse operations. When combining x terms like 3x and 4x, we add them because they are like terms with the same sign, getting 7x on the left side.

To move 10x from the right to the left, we subtract 10x from both sides because we want the opposite of adding 10x. This follows the rule of inverse operations, where subtraction is the inverse of addition. After subtraction, the equation looks like 7x - 10x = -6 + 10, which simplifies to -3x = 4. Finally, to solve for x, we divide both sides by -3, the coefficient of x, because division is the inverse of multiplication. This yields x = -4/3.

In summary, knowing whether to add or subtract when combining terms depends on what operation will help isolate the variable x. We use inverse operations to move terms across the equation: adding opposite terms cancels out, while subtracting like terms consolidates them. To check the reasonableness of our solution, we can plug x back into the original equation and confirm that both sides are equal.