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How Can You Solve a Variable in an Expression?

A variable is a placeholder. It represents a value, or number, that can change depending on the operations and numbers, or constants, in an expression. A constant is the opposite of a variable. As its name suggests, a constant never changes. In the expression x + 1, x is a variable and 1 is a constant. Mathematicians refer to both variables and constants as "terms." When you solve for the variable in an expression, you are trying to discover the value of that variable.

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Instructions

- 1
  Write the expression you want to analyze. For example, write 3x - 7.
- 2
  Set the expression equal to a number in terms of which you want to solve the variable in the expression. For example, you set your expression equal to two: 3x - 7 = 2.
- 3
  Identify an addition or subtraction operation to perform on both sides of the equation you have created that will leave your variable term alone on its side of the equation. For example, the term containing the variable in this equation is 3x. You note that adding 7 to both sides of the equation will leave the 3x term alone on the left side of the equation.
- 4
  Perform the operation you have identified. For example, 3x - 7 + 7 = 2 + 7.
- 5
  Simply your equation by completing the operation. For example, 3x = 9.
- 6
  Identify the coefficient of your variable term. The coefficient of a variable is any term immediately to the left of the variable. For example, the coefficient of x in your equation is 3.
- 7
  Multiply both sides of your equation by the reciprocal of the coefficient you have identified. The reciprocal of a number is 1 over that number. The reciprocal of 2 is 1/2 and the reciprocal of 1/2 is 1/(1/2), or two. For example, the reciprocal of the coefficient in your equation, 3, is 1/3: 1/3 * 3x = 1/3 * 9.
- 8
  Simply your equation by completing the operation. Remember that the product of any number and its reciprocal is 1. For example, the product of 3 and its reciprocal, 1/3, is 1. Your simplified equation becomes x = 3. Solving for the variable in your expression in terms of two, you have learned that the variable, x, is equal to 3.

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