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Solving equations
Use inversion of operators
When solving equations we frequently make use of the operator inversion rules to find the solutions.
Example: inversion of addition
For example, the equation 9 = 3 + x has the solution 6 (x is equal to
6). To arrive at this, we can use the inverse of the main operator in the
equation (addition): 9-3 = 6.
Example: inversion of subtraction
Now consider 19 = x - 3. The solution to this equation is 22 (x is equal
to 22). To arrive at this, we can use the inverse of the main operator in the
equation (subtraction): 19 + 3 = 22.
Example: inversion of division
The equation we want to solve: \frac{x}{6} = 4
Now we invert it by multiplying the denominator by the quotient:
6\cdot 4 = 24. Therefore: \frac{24}{6} = 4
The solution is 24
Example: inversion of multiplication
The equation we want to solve: 4x = 36 Now we invert it by dividing the
product by the coefficient: !Add link to 'coefficient'
\frac{36}{4} = 9Therefore the solution is 9: 4(9) = 36