Finite Math Examples

$x = 50 x$ , $x = 11000 + 27 x$

Step 1

Eliminate the equal sides of each equation and combine.

$50 x = 11000 + 27 x$

Step 2

Solve $50 x = 11000 + 27 x$ for $x$ .

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Step 2.1

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

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Step 2.1.1

Subtract $27 x$ from both sides of the equation.

$50 x - 27 x = 11000$

Step 2.1.2

Subtract $27 x$ from $50 x$ .

$23 x = 11000$

Step 2.2

Divide each term in $23 x = 11000$ by $23$ and simplify.

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Step 2.2.1

Divide each term in $23 x = 11000$ by $23$ .

$\frac{23 x}{23} = \frac{11000}{23}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $23$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{23 x}{23} = \frac{11000}{23}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{11000}{23}$

Step 3

Evaluate $x$ when $x = \frac{11000}{23}$ .

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Step 3.1

Substitute $\frac{11000}{23}$ for $x$ .

$\frac{11000}{23} = 11000 + 27 (\frac{11000}{23})$

Step 3.2

Substitute $\frac{11000}{23}$ for $x$ in $\frac{11000}{23} = 11000 + 27 (\frac{11000}{23})$ and solve for $x$ .

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Step 3.2.1

Simplify $11000 + 27 (\frac{11000}{23})$ .

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Step 3.2.1.1

Multiply $27 (\frac{11000}{23})$ .

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Step 3.2.1.1.1

Combine $27$ and $\frac{11000}{23}$ .

$\frac{11000}{23} = 11000 + \frac{27 \cdot 11000}{23}$

Step 3.2.1.1.2

Multiply $27$ by $11000$ .

$\frac{11000}{23} = 11000 + \frac{297000}{23}$

Step 3.2.1.2

To write $11000$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$\frac{11000}{23} = 11000 \cdot \frac{23}{23} + \frac{297000}{23}$

Step 3.2.1.3

Combine $11000$ and $\frac{23}{23}$ .

$\frac{11000}{23} = \frac{11000 \cdot 23}{23} + \frac{297000}{23}$

Step 3.2.1.4

Combine the numerators over the common denominator.

$\frac{11000}{23} = \frac{11000 \cdot 23 + 297000}{23}$

Step 3.2.1.5

Simplify the numerator.

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Step 3.2.1.5.1

Multiply $11000$ by $23$ .

$\frac{11000}{23} = \frac{253000 + 297000}{23}$

Step 3.2.1.5.2

Add $253000$ and $297000$ .

$\frac{11000}{23} = \frac{550000}{23}$

Step 3.2.2

Since $\frac{11000}{23} \neq \frac{550000}{23}$ , there are no solutions.

No solution

Step 4

The solution of the system of equations is all the values that make the system true.

No solution

Step 5