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Solving Equations

Take a look at the equation below. As you can see, after the variable is subtracted from the left and the constants are subtracted from the right, you are still left with 2x on one side.

Initial Equation / Problem x + 23 = 3x + 45
 
Subtract x from each side x - x + 23 = 3x - x + 45
Result 23 = 2x + 45
 
 
Subtract 45 from each side 23 - 45 = 2x + 45 - 45
Result -22 = 2x
 
Switch the left and right sides of the equation 2x = -22

This means that the unknown number multiplied by two, equals -22. To find the value of x, use the process "dividing by the coefficient" described on the next page.

Identifying and Using Coefficients

The coefficient of a variable is the number which the variable is being multiplied by. In this equation, 2 is the coefficient of x because 2x is present in the equation. Some additional examples of coefficients:

Term Coefficient of x
2x 2
0.24x 0.24
x 1
-x -1

Note that in the last two examples, the following rules are applied

  • If the variable has no visible coefficient, then it has an implied coefficient of 1.
  • If the variable only has a negative sign, then it has an implied coefficient of -1.

Continue to the next page to see how we use the coefficient of the variable x in the equation, 2, to find the value of x.


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