39 lines
1.1 KiB
Markdown
39 lines
1.1 KiB
Markdown
---
|
|
tags:
|
|
- Mathematics
|
|
- Algebra
|
|
- operators
|
|
---
|
|
|
|
## Use inversion of operators
|
|
|
|
When solving equations we frequently make use of the [ operator inversion rules](../Prealgebra/Inversion%20of%20operators.md) 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 $9$:
|
|
$$ 4(9) = 36$$
|