Finite Math Examples

$\frac{3}{2} \cdot (x + 4) + 2 x - 3 = 10$

Step 1

Simplify $\frac{3}{2} \cdot (x + 4) + 2 x - 3$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{3}{2} x + \frac{3}{2} \cdot 4 + 2 x - 3 = 10$

Step 1.1.2

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} + \frac{3}{2} \cdot 4 + 2 x - 3 = 10$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $4$ .

$\frac{3 x}{2} + \frac{3}{2} \cdot (2 (2)) + 2 x - 3 = 10$

Step 1.1.3.2

Cancel the common factor.

$\frac{3 x}{2} + \frac{3}{2} \cdot (2 \cdot 2) + 2 x - 3 = 10$

Step 1.1.3.3

Rewrite the expression.

$\frac{3 x}{2} + 3 \cdot 2 + 2 x - 3 = 10$

Step 1.1.4

Multiply $3$ by $2$ .

$\frac{3 x}{2} + 6 + 2 x - 3 = 10$

Step 1.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} + 2 x \cdot \frac{2}{2} + 6 - 3 = 10$

Step 1.3

Combine $2 x$ and $\frac{2}{2}$ .

$\frac{3 x}{2} + \frac{2 x \cdot 2}{2} + 6 - 3 = 10$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 x + 2 x \cdot 2}{2} + 6 - 3 = 10$

Step 1.5

Find the common denominator.

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Step 1.5.1

Write $6$ as a fraction with denominator $1$ .

$\frac{3 x + 2 x \cdot 2}{2} + \frac{6}{1} - 3 = 10$

Step 1.5.2

Multiply $\frac{6}{1}$ by $\frac{2}{2}$ .

$\frac{3 x + 2 x \cdot 2}{2} + \frac{6}{1} \cdot \frac{2}{2} - 3 = 10$

Step 1.5.3

Multiply $\frac{6}{1}$ by $\frac{2}{2}$ .

$\frac{3 x + 2 x \cdot 2}{2} + \frac{6 \cdot 2}{2} - 3 = 10$

Step 1.5.4

Write $- 3$ as a fraction with denominator $1$ .

$\frac{3 x + 2 x \cdot 2}{2} + \frac{6 \cdot 2}{2} + \frac{- 3}{1} = 10$

Step 1.5.5

Multiply $\frac{- 3}{1}$ by $\frac{2}{2}$ .

$\frac{3 x + 2 x \cdot 2}{2} + \frac{6 \cdot 2}{2} + \frac{- 3}{1} \cdot \frac{2}{2} = 10$

Step 1.5.6

Multiply $\frac{- 3}{1}$ by $\frac{2}{2}$ .

$\frac{3 x + 2 x \cdot 2}{2} + \frac{6 \cdot 2}{2} + \frac{- 3 \cdot 2}{2} = 10$

Step 1.6

Combine the numerators over the common denominator.

$\frac{3 x + 2 x \cdot 2 + 6 \cdot 2 - 3 \cdot 2}{2} = 10$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $2$ by $2$ .

$\frac{3 x + 4 x + 6 \cdot 2 - 3 \cdot 2}{2} = 10$

Step 1.7.2

Multiply $6$ by $2$ .

$\frac{3 x + 4 x + 12 - 3 \cdot 2}{2} = 10$

Step 1.7.3

Multiply $- 3$ by $2$ .

$\frac{3 x + 4 x + 12 - 6}{2} = 10$

Step 1.8

Simplify by adding terms.

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Step 1.8.1

Add $3 x$ and $4 x$ .

$\frac{7 x + 12 - 6}{2} = 10$

Step 1.8.2

Subtract $6$ from $12$ .

$\frac{7 x + 6}{2} = 10$

Step 2

Multiply both sides by $2$ .

$\frac{7 x + 6}{2} \cdot 2 = 10 \cdot 2$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{7 x + 6}{2} \cdot 2 = 10 \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$7 x + 6 = 10 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $10$ by $2$ .

$7 x + 6 = 20$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $6$ from both sides of the equation.

$7 x = 20 - 6$

Step 4.1.2

Subtract $6$ from $20$ .

$7 x = 14$

Step 4.2

Divide each term in $7 x = 14$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 x = 14$ by $7$ .

$\frac{7 x}{7} = \frac{14}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{14}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $14$ by $7$ .

$x = 2$