Finite Math Examples

$- 10 x \cdot 1 - 30 x \cdot 2 + 26 x \cdot 3 = 1$ , $15 x \cdot 1 + 31 x \cdot 2 - 11 x \cdot 3 = - 28$ , $- 10 x \cdot 1 + 4 x \cdot 2 = - 11$

Step 1

Divide each term in $8 x = 1$ by $8$ and simplify.

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Step 1.1

Divide each term in $8 x = 1$ by $8$ .

$\frac{8 x}{8} = \frac{1}{8}$

$44 x = - 28$

$- 2 x = - 11$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $8$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{1}{8}$

$44 x = - 28$

$- 2 x = - 11$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{8}$

$44 x = - 28$

$- 2 x = - 11$

$x = \frac{1}{8}$

$44 x = - 28$

$- 2 x = - 11$

$x = \frac{1}{8}$

$44 x = - 28$

$- 2 x = - 11$

$x = \frac{1}{8}$

$44 x = - 28$

$- 2 x = - 11$

Step 2

Replace all occurrences of $x$ with $\frac{1}{8}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $44 x = - 28$ with $\frac{1}{8}$ .

$44 (\frac{1}{8}) = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $44 (\frac{1}{8})$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Factor $4$ out of $44$ .

$4 (11) (\frac{1}{8}) = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

Step 2.2.1.1.2

Factor $4$ out of $8$ .

$4 \cdot (11 (\frac{1}{4 \cdot 2})) = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

Step 2.2.1.1.3

Cancel the common factor.

$4 \cdot (11 (\frac{1}{4 \cdot 2})) = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

Step 2.2.1.1.4

Rewrite the expression.

$11 (\frac{1}{2}) = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

$11 (\frac{1}{2}) = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

Step 2.2.1.2

Combine $11$ and $\frac{1}{2}$ .

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

$- 2 x = - 11$

Step 2.3

Replace all occurrences of $x$ in $- 2 x = - 11$ with $\frac{1}{8}$ .

$- 2 (\frac{1}{8}) = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $- 2 (\frac{1}{8})$ .

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Step 2.4.1.1

Cancel the common factor of $2$ .

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Step 2.4.1.1.1

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{1}{8}) = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

Step 2.4.1.1.2

Factor $2$ out of $8$ .

$2 \cdot (- 1 \frac{1}{2 \cdot 4}) = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

Step 2.4.1.1.3

Cancel the common factor.

$2 \cdot (- 1 \frac{1}{2 \cdot 4}) = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

Step 2.4.1.1.4

Rewrite the expression.

$- 1 (\frac{1}{4}) = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

$- 1 (\frac{1}{4}) = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

Step 2.4.1.2

Rewrite $- 1 (\frac{1}{4})$ as $- (\frac{1}{4})$ .

$- \frac{1}{4} = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

$- \frac{1}{4} = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

$- \frac{1}{4} = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

$- \frac{1}{4} = - 11$

$\frac{11}{2} = - 28$

$x = \frac{1}{8}$

Step 3

Since $- \frac{1}{4} = - 11$ is not true, there is no solution.

No solution

Step 4