Finite Math Examples

$p = - 4 x + 250$ , $p = 3 x + 40$

Step 1

Eliminate the equal sides of each equation and combine.

$- 4 x + 250 = 3 x + 40$

Step 2

Solve $- 4 x + 250 = 3 x + 40$ 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 $3 x$ from both sides of the equation.

$- 4 x + 250 - 3 x = 40$

Step 2.1.2

Subtract $3 x$ from $- 4 x$ .

$- 7 x + 250 = 40$

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 $250$ from both sides of the equation.

$- 7 x = 40 - 250$

Step 2.2.2

Subtract $250$ from $40$ .

$- 7 x = - 210$

Step 2.3

Divide each term in $- 7 x = - 210$ by $- 7$ and simplify.

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Step 2.3.1

Divide each term in $- 7 x = - 210$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 210}{- 7}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 210}{- 7}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 210}{- 7}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 210$ by $- 7$ .

$x = 30$

Step 3

Evaluate $p$ when $x = 30$ .

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Step 3.1

Substitute $30$ for $x$ .

$p = 3 (30) + 40$

Step 3.2

Simplify $3 (30) + 40$ .

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Step 3.2.1

Multiply $3$ by $30$ .

$p = 90 + 40$

Step 3.2.2

Add $90$ and $40$ .

$p = 130$

Step 4

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

$p = 130, x = 30$