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