Finite Math Examples

$x = 0.2 x + 120$ , $x = 0.4 x$

Step 1

Eliminate the equal sides of each equation and combine.

$0.2 x + 120 = 0.4 x$

Step 2

Solve $0.2 x + 120 = 0.4 x$ 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 $0.4 x$ from both sides of the equation.

$0.2 x + 120 - 0.4 x = 0$

Step 2.1.2

Subtract $0.4 x$ from $0.2 x$ .

$- 0.2 x + 120 = 0$

Step 2.2

Subtract $120$ from both sides of the equation.

$- 0.2 x = - 120$

Step 2.3

Divide each term in $- 0.2 x = - 120$ by $- 0.2$ and simplify.

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Step 2.3.1

Divide each term in $- 0.2 x = - 120$ by $- 0.2$ .

$\frac{- 0.2 x}{- 0.2} = \frac{- 120}{- 0.2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 0.2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 0.2 x}{- 0.2} = \frac{- 120}{- 0.2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 120}{- 0.2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 120$ by $- 0.2$ .

$x = 600$

Step 3

Evaluate $x$ when $x = 600$ .

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Step 3.1

Substitute $600$ for $x$ .

$600 = 0.4 (600)$

Step 3.2

Substitute $600$ for $x$ in $600 = 0.4 (600)$ and solve for $x$ .

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Step 3.2.1

Multiply $0.4$ by $600$ .

$600 = 240$

Step 3.2.2

Since $600 \neq 240$ , 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