40 lines
1.1 KiB
Markdown
40 lines
1.1 KiB
Markdown
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---
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tags:
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- Mathematics
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- Algebra
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- operators
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---
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## Use inversion of operators
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When solving equations we frequently make use of the [ operator inversion rules](../Prealgebra/Inversion%20of%20operators.md) to find the solutions.
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### Example: inversion of addition
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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): $9-3 = 6$.
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### Example: inversion of subtraction
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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): $19 + 3 = 22$.
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### Example: inversion of division
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The equation we want to solve:
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$$\frac{x}{6} = 4$$
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Now we invert it by multiplying the denominator by the quotient: $6\cdot 4 = 24$. Therefore:
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$$ \frac{24}{6} = 4$$
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The solution is $24$
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### Example: inversion of multiplication
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The equation we want to solve:
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$$4x = 36$$
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Now we invert it by dividing the product by the coefficient:
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!Add link to 'coefficient'
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$$\frac{36}{4} = 9$$
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Therefore the solution is $9$:
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$$ 4(9) = 36$$
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