Algebra Examples

$\frac{3 x - 2}{5} - \frac{4 x + 3}{6} = - 1$

Step 1

Simplify $\frac{3 x - 2}{5} - \frac{4 x + 3}{6}$ .

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Step 1.1

To write $\frac{3 x - 2}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{3 x - 2}{5} \cdot \frac{6}{6} - \frac{4 x + 3}{6} = - 1$

Step 1.2

To write $- \frac{4 x + 3}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x - 2}{5} \cdot \frac{6}{6} - \frac{4 x + 3}{6} \cdot \frac{5}{5} = - 1$

Step 1.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 x - 2}{5}$ by $\frac{6}{6}$ .

$\frac{(3 x - 2) \cdot 6}{5 \cdot 6} - \frac{4 x + 3}{6} \cdot \frac{5}{5} = - 1$

Step 1.3.2

Multiply $5$ by $6$ .

$\frac{(3 x - 2) \cdot 6}{30} - \frac{4 x + 3}{6} \cdot \frac{5}{5} = - 1$

Step 1.3.3

Multiply $\frac{4 x + 3}{6}$ by $\frac{5}{5}$ .

$\frac{(3 x - 2) \cdot 6}{30} - \frac{(4 x + 3) \cdot 5}{6 \cdot 5} = - 1$

Step 1.3.4

Multiply $6$ by $5$ .

$\frac{(3 x - 2) \cdot 6}{30} - \frac{(4 x + 3) \cdot 5}{30} = - 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(3 x - 2) \cdot 6 - (4 x + 3) \cdot 5}{30} = - 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{3 x \cdot 6 - 2 \cdot 6 - (4 x + 3) \cdot 5}{30} = - 1$

Step 1.5.2

Multiply $6$ by $3$ .

$\frac{18 x - 2 \cdot 6 - (4 x + 3) \cdot 5}{30} = - 1$

Step 1.5.3

Multiply $- 2$ by $6$ .

$\frac{18 x - 12 - (4 x + 3) \cdot 5}{30} = - 1$

Step 1.5.4

Apply the distributive property.

$\frac{18 x - 12 + (- (4 x) - 1 \cdot 3) \cdot 5}{30} = - 1$

Step 1.5.5

Multiply $4$ by $- 1$ .

$\frac{18 x - 12 + (- 4 x - 1 \cdot 3) \cdot 5}{30} = - 1$

Step 1.5.6

Multiply $- 1$ by $3$ .

$\frac{18 x - 12 + (- 4 x - 3) \cdot 5}{30} = - 1$

Step 1.5.7

Apply the distributive property.

$\frac{18 x - 12 - 4 x \cdot 5 - 3 \cdot 5}{30} = - 1$

Step 1.5.8

Multiply $5$ by $- 4$ .

$\frac{18 x - 12 - 20 x - 3 \cdot 5}{30} = - 1$

Step 1.5.9

Multiply $- 3$ by $5$ .

$\frac{18 x - 12 - 20 x - 15}{30} = - 1$

Step 1.5.10

Subtract $20 x$ from $18 x$ .

$\frac{- 2 x - 12 - 15}{30} = - 1$

Step 1.5.11

Subtract $15$ from $- 12$ .

$\frac{- 2 x - 27}{30} = - 1$

Step 1.6

Simplify with factoring out.

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Step 1.6.1

Factor $- 1$ out of $- 2 x$ .

$\frac{- (2 x) - 27}{30} = - 1$

Step 1.6.2

Rewrite $- 27$ as $- 1 (27)$ .

$\frac{- (2 x) - 1 (27)}{30} = - 1$

Step 1.6.3

Factor $- 1$ out of $- (2 x) - 1 (27)$ .

$\frac{- (2 x + 27)}{30} = - 1$

Step 1.6.4

Simplify the expression.

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Step 1.6.4.1

Rewrite $- (2 x + 27)$ as $- 1 (2 x + 27)$ .

$\frac{- 1 (2 x + 27)}{30} = - 1$

Step 1.6.4.2

Move the negative in front of the fraction.

$- \frac{2 x + 27}{30} = - 1$

Step 2

Multiply both sides of the equation by $- 30$ .

$- 30 (- \frac{2 x + 27}{30}) = - 30 \cdot - 1$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 30 (- \frac{2 x + 27}{30})$ .

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Step 3.1.1.1

Cancel the common factor of $30$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{2 x + 27}{30}$ into the numerator.

$- 30 \frac{- (2 x + 27)}{30} = - 30 \cdot - 1$

Step 3.1.1.1.2

Factor $30$ out of $- 30$ .

$30 (- 1) \frac{- (2 x + 27)}{30} = - 30 \cdot - 1$

Step 3.1.1.1.3

Cancel the common factor.

$30 \cdot - 1 \frac{- (2 x + 27)}{30} = - 30 \cdot - 1$

Step 3.1.1.1.4

Rewrite the expression.

$- - (2 x + 27) = - 30 \cdot - 1$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (2 x + 27) = - 30 \cdot - 1$

Step 3.1.1.2.2

Multiply $2 x + 27$ by $1$ .

$2 x + 27 = - 30 \cdot - 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 30$ by $- 1$ .

$2 x + 27 = 30$

Step 4

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

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Step 4.1

Subtract $27$ from both sides of the equation.

$2 x = 30 - 27$

Step 4.2

Subtract $27$ from $30$ .

$2 x = 3$

Step 5

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 3$ by $2$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$