Finite Math Examples

$x \cdot 1 + 2 x \cdot 2 - x \cdot 3 = 3$ , $2 x \cdot 1 + 3 x \cdot 2 - x \cdot 3 = 5$ , $3 x \cdot 1 + 5 x \cdot 2 - 2 x \cdot 3 = 8$

Step 1

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

$5 x = 5$

$7 x = 8$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

$5 x = 5$

$7 x = 8$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

$5 x = 5$

$7 x = 8$

$x = \frac{3}{2}$

$5 x = 5$

$7 x = 8$

$x = \frac{3}{2}$

$5 x = 5$

$7 x = 8$

$x = \frac{3}{2}$

$5 x = 5$

$7 x = 8$

Step 2

Replace all occurrences of $x$ with $\frac{3}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $5 x = 5$ with $\frac{3}{2}$ .

$5 (\frac{3}{2}) = 5$

$x = \frac{3}{2}$

$7 x = 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $5 (\frac{3}{2})$ .

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Step 2.2.1.1

Combine $5$ and $\frac{3}{2}$ .

$\frac{5 \cdot 3}{2} = 5$

$x = \frac{3}{2}$

$7 x = 8$

Step 2.2.1.2

Multiply $5$ by $3$ .

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

$7 x = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

$7 x = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

$7 x = 8$

Step 2.3

Replace all occurrences of $x$ in $7 x = 8$ with $\frac{3}{2}$ .

$7 (\frac{3}{2}) = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Multiply $7 (\frac{3}{2})$ .

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Step 2.4.1.1

Combine $7$ and $\frac{3}{2}$ .

$\frac{7 \cdot 3}{2} = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

Step 2.4.1.2

Multiply $7$ by $3$ .

$\frac{21}{2} = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

$\frac{21}{2} = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

$\frac{21}{2} = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

$\frac{21}{2} = 8$

$\frac{15}{2} = 5$

$x = \frac{3}{2}$

Step 3

Since $\frac{21}{2} = 8$ is not true, there is no solution.

No solution

Step 4