Finite Math Examples

$u = i - j$ , $v = 3 i + 5 j$

Step 1

Reorder $i$ and $- j$ .

$u = - j + i$

$v = 3 i + 5 j$

Step 2

Reorder $3 i$ and $5 j$ .

$v = 5 j + 3 i$

$u = - j + i$

Step 3

Solve the equation for $i$ .

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Step 3.1

Remove parentheses.

$- j + i = i - j$

$u = - j + i$

Step 3.2

Move all terms containing $i$ to the left side of the equation.

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Step 3.2.1

Subtract $i$ from both sides of the equation.

$- j + i - i = - j$

$u = - j + i$

Step 3.2.2

Combine the opposite terms in $- j + i - i$ .

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Step 3.2.2.1

Subtract $i$ from $i$ .

$- j + 0 = - j$

$u = - j + i$

Step 3.2.2.2

Add $- j$ and $0$ .

$- j = - j$

$u = - j + i$

$- j = - j$

$u = - j + i$

$- j = - j$

$u = - j + i$

Step 3.3

Divide each term in $- j = - j$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- j = - j$ by $- 1$ .

$\frac{- j}{- 1} = \frac{- j}{- 1}$

$u = - j + i$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{j}{1} = \frac{- j}{- 1}$

$u = - j + i$

Step 3.3.2.2

Divide $j$ by $1$ .

$j = \frac{- j}{- 1}$

$u = - j + i$

$j = \frac{- j}{- 1}$

$u = - j + i$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$j = \frac{j}{1}$

$u = - j + i$

Step 3.3.3.2

Divide $j$ by $1$ .

$j = j$

$u = - j + i$

$j = j$

$u = - j + i$

$j = j$

$u = - j + i$

Step 3.4

The variable $i$ got canceled.

All real numbers

$u = - j + i$

All real numbers

$u = - j + i$