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To solve an equation with variables on each side, such as –9 + 3x = 8x + 6, you always first need to add or subtract the variable terms from each side.

User Mariselvam
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Answer:

False

Explanation:

You want to know if it is true that to solve an equation with variables on each side, such as –9 + 3x = 8x + 6, you always first need to add or subtract the variable terms from each side.

3-Step equation

The equation described here, with variable and constant terms on both sides, can be called a 3-step linear equation, because it typically takes 3 steps to solve it.

The first step is to choose one of the variable terms, and subtract that from both sides. We like to choose the term with the lowest coefficient, so the result will be a variable term with a positive coefficient.

-9 +3x = 8x +6 . . . . . . original equation

Term 3x has the lowest coefficient, so we choose to subtract 3x from both sides:

-9 +3x -3x = 8x -3x +6

-9 = 5x +6

The offered statement is false. You need to subtract one of the variable terms from each side.

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Additional comment

The second step is to subtract the constant that is on the same side of the equal sign as the variable term. Here, that means subtract 6.

-9 -6 = 5x +6 -6

-15 = 5x

Note that we have subtracted two terms from both sides of the equation:

  • the variable term with the smallest coefficient
  • the constant term on the side with the variable having the largest coefficient

These subtractions can be done in either order, or both at once. It is incorrect to say that one of them must be done first.

-9 +3x = 8x +6

-9 +3x -(3x+6) = 8x +6 -(3x +6) . . . . subtract both unwanted terms

-15 = 5x . . . . . . . simplified

The third step is to divide by the coefficient of the variable.

-15/5 = 5x/5

-3 = x

When learning to solve equations of this sort, it is nice to have a reliable set of steps to follow. That is why adding the opposite of an unwanted variable term is recommended as a first step. In math, there are usually a number of ways a problem can be solved, so any "always do this first" instruction probably should be considered to be advice that may not need to be followed.

User Etoisarobot
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