The variable, usually x{\displaystyle x}, represents an unknown value. Solving an equation means finding the unknown value. The equation may also have a coefficient, which is a number you need to multiply by the variable to equal a certain product. The variable may also be the numerator of a fraction. This means you need to divide the variable by the number in the denominator to equal a certain quotient.

For example, you might have the equation 3x=24{\displaystyle 3x=24}. The variable representing the unknown number is x{\displaystyle x}. When you multiply the unknown number and 3, the product is 24.
 Isolating a variable means getting it by itself on one side of the equation. To do this you must perform an inverse operation to cancel coefficients or fractions. Multiplication and division are inverse operations. If the variable has a coefficient, to cancel it you would divide by the coefficient, since any number divided by itself is equal to 1. If the variable is the numerator of a fraction, to isolate it you would multiply by the denominator, since multiplying by a number cancels the division by that number.For example, in the equation 3x=24{\displaystyle 3x=24} the variable is multiplied by 3, so to isolate the variable you must cancel the 3 by dividing by 3.
 As you solve an equation the most important thing to remember is that you must keep both sides of the equation balanced. This means that whatever you do to one side of the equation, you must do to the other side, too.So, if you need to divide by a value to isolate the variable, you must also divide by the same value on the other side of the equation.

For example, in the equation 3x=24{\displaystyle 3x=24}, you need to divide by 3 on the left side to isolate the variable, so you also need to divide by 3 on the right side of the equation:3x=24{\displaystyle 3x=24}3x3=243{\displaystyle {\frac {3x}{3}}={\frac {24}{3}}}x=8{\displaystyle x=8}


, To make sure your answer is correct, plug the value of x{\displaystyle x} into the original equation. If the equation is true, your solution is correct.

For example, if you found that x=8{\displaystyle x=8}, substitute 8 for x{\displaystyle x} in the original equation: 3(8)=24{\displaystyle 3(8)=24}. Since this equation is true, your solution is correct.
Evaluate the equation.
Determine how to isolate the variable.
Multiply or divide from both sides of the equation.
Check your solution.
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