Algebra Examples

$\frac{x - 3}{5} - \frac{4 - 3 x}{3} = \frac{2}{15}$

Step 1

Simplify $\frac{x - 3}{5} - \frac{4 - 3 x}{3}$ .

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Step 1.1

To write $\frac{x - 3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x - 3}{5} \cdot \frac{3}{3} - \frac{4 - 3 x}{3} = \frac{2}{15}$

Step 1.2

To write $- \frac{4 - 3 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x - 3}{5} \cdot \frac{3}{3} - \frac{4 - 3 x}{3} \cdot \frac{5}{5} = \frac{2}{15}$

Step 1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x - 3}{5}$ by $\frac{3}{3}$ .

$\frac{(x - 3) \cdot 3}{5 \cdot 3} - \frac{4 - 3 x}{3} \cdot \frac{5}{5} = \frac{2}{15}$

Step 1.3.2

Multiply $5$ by $3$ .

$\frac{(x - 3) \cdot 3}{15} - \frac{4 - 3 x}{3} \cdot \frac{5}{5} = \frac{2}{15}$

Step 1.3.3

Multiply $\frac{4 - 3 x}{3}$ by $\frac{5}{5}$ .

$\frac{(x - 3) \cdot 3}{15} - \frac{(4 - 3 x) \cdot 5}{3 \cdot 5} = \frac{2}{15}$

Step 1.3.4

Multiply $3$ by $5$ .

$\frac{(x - 3) \cdot 3}{15} - \frac{(4 - 3 x) \cdot 5}{15} = \frac{2}{15}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(x - 3) \cdot 3 - (4 - 3 x) \cdot 5}{15} = \frac{2}{15}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{x \cdot 3 - 3 \cdot 3 - (4 - 3 x) \cdot 5}{15} = \frac{2}{15}$

Step 1.5.2

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

$\frac{3 \cdot x - 3 \cdot 3 - (4 - 3 x) \cdot 5}{15} = \frac{2}{15}$

Step 1.5.3

Multiply $- 3$ by $3$ .

$\frac{3 \cdot x - 9 - (4 - 3 x) \cdot 5}{15} = \frac{2}{15}$

Step 1.5.4

Apply the distributive property.

$\frac{3 x - 9 + (- 1 \cdot 4 - (- 3 x)) \cdot 5}{15} = \frac{2}{15}$

Step 1.5.5

Multiply $- 1$ by $4$ .

$\frac{3 x - 9 + (- 4 - (- 3 x)) \cdot 5}{15} = \frac{2}{15}$

Step 1.5.6

Multiply $- 3$ by $- 1$ .

$\frac{3 x - 9 + (- 4 + 3 x) \cdot 5}{15} = \frac{2}{15}$

Step 1.5.7

Apply the distributive property.

$\frac{3 x - 9 - 4 \cdot 5 + 3 x \cdot 5}{15} = \frac{2}{15}$

Step 1.5.8

Multiply $- 4$ by $5$ .

$\frac{3 x - 9 - 20 + 3 x \cdot 5}{15} = \frac{2}{15}$

Step 1.5.9

Multiply $5$ by $3$ .

$\frac{3 x - 9 - 20 + 15 x}{15} = \frac{2}{15}$

Step 1.5.10

Add $3 x$ and $15 x$ .

$\frac{18 x - 9 - 20}{15} = \frac{2}{15}$

Step 1.5.11

Subtract $20$ from $- 9$ .

$\frac{18 x - 29}{15} = \frac{2}{15}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$18 x - 29 = 2$

Step 3

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

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Step 3.1

Add $29$ to both sides of the equation.

$18 x = 2 + 29$

Step 3.2

Add $2$ and $29$ .

$18 x = 31$

Step 4

Divide each term in $18 x = 31$ by $18$ and simplify.

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Step 4.1

Divide each term in $18 x = 31$ by $18$ .

$\frac{18 x}{18} = \frac{31}{18}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $18$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{18 x}{18} = \frac{31}{18}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{31}{18}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{31}{18}$

Decimal Form:

$x = 1.7\overline{2}$

Mixed Number Form:

$x = 1 \frac{13}{18}$