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’

$$\frac{36}{4} = 9$$

Therefore the solution is \(9\): $$ 4(9) = 36$$