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How to Solve Linear Relations

The word "relation" comes from the idea of a relationship. In math, relations describe how one variable is related to numbers or to another variable . Linear relations are a specific type for which the relationship represents a line. You can tell a relation is linear if it does not have variables raised to exponents, variables in the denominator, radicals, nor absolute values. Solving linear relations involves isolating the variable so that you can find its numerical value. This is the number that would make the relationship true.

Instructions

    • 1

      Distribute any numbers outside of parenthesis by multiplying them by each term on the inside. For instance, with 5(3X - 2) + 4 = 24 - 6X you multiply 5 with 3X and 5 with -2 to get 15X - 10 + 4 = 24 - 6X.

    • 2

      Combine any like terms (either variables or numbers). For example, -10 and 4 combine so that you get 15X -6 = 24 - 6X.

    • 3

      Identify the smaller amount of the variable; in 15X -6 = 24 - 6X it would be 6X. Then, perform the opposite operation of what is in front of it to both sides. Here, you would add 6X to both sides to get 21X - 6 = 24.

    • 4

      Determine if there are any constants (numbers not attached to the variable) on the side with the variable. If you find one, perform the opposite operation with it to both sides. With 21X - 6 = 24, you add 6 to both sides and end up with 21X = 30.

    • 5

      Divide both sides by the number in front of the variable. For example, divide both sides of 21X = 30 by 21 to get X = 30/21. If the result is a fraction, reduce it if possible by dividing both the top and bottom number by the same thing. Here, divide both 30 and 21 by 3 to arrive at X = 10/7.

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