Finite Math Examples

$2 x - 6 (5 - \frac{5 x}{2}) = 7$

Step 1

Simplify $2 x - 6 (5 - \frac{5 x}{2})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 x - 6 \cdot 5 - 6 (- \frac{5 x}{2}) = 7$

Step 1.1.2

Multiply $- 6$ by $5$ .

$2 x - 30 - 6 (- \frac{5 x}{2}) = 7$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$2 x - 30 - 6 \frac{- 5 x}{2} = 7$

Step 1.1.3.2

Factor $2$ out of $- 6$ .

$2 x - 30 + 2 (- 3) \frac{- 5 x}{2} = 7$

Step 1.1.3.3

Cancel the common factor.

$2 x - 30 + 2 \cdot - 3 \frac{- 5 x}{2} = 7$

Step 1.1.3.4

Rewrite the expression.

$2 x - 30 - 3 (- 5 x) = 7$

Step 1.1.4

Multiply $- 5$ by $- 3$ .

$2 x - 30 + 15 x = 7$

Step 1.2

Add $2 x$ and $15 x$ .

$17 x - 30 = 7$

Step 2

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

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Step 2.1

Add $30$ to both sides of the equation.

$17 x = 7 + 30$

Step 2.2

Add $7$ and $30$ .

$17 x = 37$

Step 3

Divide each term in $17 x = 37$ by $17$ and simplify.

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Step 3.1

Divide each term in $17 x = 37$ by $17$ .

$\frac{17 x}{17} = \frac{37}{17}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $17$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{17 x}{17} = \frac{37}{17}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{37}{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{37}{17}$

Decimal Form:

$x = 2.17647058 \dots$

Mixed Number Form:

$x = 2 \frac{3}{17}$