Finite Math Examples

$3 x - \frac{x}{3} + \frac{x + 1}{7} = 7 x$

Step 1

Simplify $3 x - \frac{x}{3} + \frac{x + 1}{7}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

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

$\frac{3 x}{1} - \frac{x}{3} + \frac{x + 1}{7} = 7 x$

Step 1.1.2

Multiply $\frac{3 x}{1}$ by $\frac{21}{21}$ .

$\frac{3 x}{1} \cdot \frac{21}{21} - \frac{x}{3} + \frac{x + 1}{7} = 7 x$

Step 1.1.3

Multiply $\frac{3 x}{1}$ by $\frac{21}{21}$ .

$\frac{3 x \cdot 21}{21} - \frac{x}{3} + \frac{x + 1}{7} = 7 x$

Step 1.1.4

Multiply $\frac{x}{3}$ by $\frac{7}{7}$ .

$\frac{3 x \cdot 21}{21} - (\frac{x}{3} \cdot \frac{7}{7}) + \frac{x + 1}{7} = 7 x$

Step 1.1.5

Multiply $\frac{x}{3}$ by $\frac{7}{7}$ .

$\frac{3 x \cdot 21}{21} - \frac{x \cdot 7}{3 \cdot 7} + \frac{x + 1}{7} = 7 x$

Step 1.1.6

Multiply $\frac{x + 1}{7}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 21}{21} - \frac{x \cdot 7}{3 \cdot 7} + \frac{x + 1}{7} \cdot \frac{3}{3} = 7 x$

Step 1.1.7

Multiply $\frac{x + 1}{7}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 21}{21} - \frac{x \cdot 7}{3 \cdot 7} + \frac{(x + 1) \cdot 3}{7 \cdot 3} = 7 x$

Step 1.1.8

Multiply $3$ by $7$ .

$\frac{3 x \cdot 21}{21} - \frac{x \cdot 7}{21} + \frac{(x + 1) \cdot 3}{7 \cdot 3} = 7 x$

Step 1.1.9

Reorder the factors of $7 \cdot 3$ .

$\frac{3 x \cdot 21}{21} - \frac{x \cdot 7}{21} + \frac{(x + 1) \cdot 3}{3 \cdot 7} = 7 x$

Step 1.1.10

Multiply $3$ by $7$ .

$\frac{3 x \cdot 21}{21} - \frac{x \cdot 7}{21} + \frac{(x + 1) \cdot 3}{21} = 7 x$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 x \cdot 21 - x \cdot 7 + (x + 1) \cdot 3}{21} = 7 x$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $21$ by $3$ .

$\frac{63 x - x \cdot 7 + (x + 1) \cdot 3}{21} = 7 x$

Step 1.3.2

Multiply $7$ by $- 1$ .

$\frac{63 x - 7 x + (x + 1) \cdot 3}{21} = 7 x$

Step 1.3.3

Apply the distributive property.

$\frac{63 x - 7 x + x \cdot 3 + 1 \cdot 3}{21} = 7 x$

Step 1.3.4

Move $3$ to the left of $x$ .

$\frac{63 x - 7 x + 3 \cdot x + 1 \cdot 3}{21} = 7 x$

Step 1.3.5

Multiply $3$ by $1$ .

$\frac{63 x - 7 x + 3 x + 3}{21} = 7 x$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Subtract $7 x$ from $63 x$ .

$\frac{56 x + 3 x + 3}{21} = 7 x$

Step 1.4.2

Add $56 x$ and $3 x$ .

$\frac{59 x + 3}{21} = 7 x$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $7 x$ from both sides of the equation.

$\frac{59 x + 3}{21} - 7 x = 0$

Step 2.2

To write $- 7 x$ as a fraction with a common denominator, multiply by $\frac{21}{21}$ .

$\frac{59 x + 3}{21} - 7 x \cdot \frac{21}{21} = 0$

Step 2.3

Combine $- 7 x$ and $\frac{21}{21}$ .

$\frac{59 x + 3}{21} + \frac{- 7 x \cdot 21}{21} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{59 x + 3 - 7 x \cdot 21}{21} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $21$ by $- 7$ .

$\frac{59 x + 3 - 147 x}{21} = 0$

Step 2.5.2

Subtract $147 x$ from $59 x$ .

$\frac{- 88 x + 3}{21} = 0$

Step 2.6

Factor $- 1$ out of $- 88 x$ .

$\frac{- (88 x) + 3}{21} = 0$

Step 2.7

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{- (88 x) - 1 (- 3)}{21} = 0$

Step 2.8

Factor $- 1$ out of $- (88 x) - 1 (- 3)$ .

$\frac{- (88 x - 3)}{21} = 0$

Step 2.9

Rewrite $- (88 x - 3)$ as $- 1 (88 x - 3)$ .

$\frac{- 1 (88 x - 3)}{21} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{88 x - 3}{21} = 0$

Step 3

Set the numerator equal to zero.

$88 x - 3 = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Add $3$ to both sides of the equation.

$88 x = 3$

Step 4.2

Divide each term in $88 x = 3$ by $88$ and simplify.

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Step 4.2.1

Divide each term in $88 x = 3$ by $88$ .

$\frac{88 x}{88} = \frac{3}{88}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $88$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{88 x}{88} = \frac{3}{88}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{88}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{88}$

Decimal Form:

$x = 0.034\overline{09}$