Finite Math Examples

$p = - 0.3 x + 6$ , $p = 0.15 x + 1.5$

Step 1

Eliminate the equal sides of each equation and combine.

$- 0.3 x + 6 = 0.15 x + 1.5$

Step 2

Solve $- 0.3 x + 6 = 0.15 x + 1.5$ 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 $0.15 x$ from both sides of the equation.

$- 0.3 x + 6 - 0.15 x = 1.5$

Step 2.1.2

Subtract $0.15 x$ from $- 0.3 x$ .

$- 0.45 x + 6 = 1.5$

Step 2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.2.1

Subtract $6$ from both sides of the equation.

$- 0.45 x = 1.5 - 6$

Step 2.2.2

Subtract $6$ from $1.5$ .

$- 0.45 x = - 4.5$

Step 2.3

Divide each term in $- 0.45 x = - 4.5$ by $- 0.45$ and simplify.

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Step 2.3.1

Divide each term in $- 0.45 x = - 4.5$ by $- 0.45$ .

$\frac{- 0.45 x}{- 0.45} = \frac{- 4.5}{- 0.45}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 0.45$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 0.45 x}{- 0.45} = \frac{- 4.5}{- 0.45}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4.5}{- 0.45}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 4.5$ by $- 0.45$ .

$x = 10$

Step 3

Evaluate $p$ when $x = 10$ .

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Step 3.1

Substitute $10$ for $x$ .

$p = 0.15 (10) + 1.5$

Step 3.2

Simplify $0.15 (10) + 1.5$ .

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Step 3.2.1

Multiply $0.15$ by $10$ .

$p = 1.5 + 1.5$

Step 3.2.2

Add $1.5$ and $1.5$ .

$p = 3$

Step 4

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

$p = 3, x = 10$