Algebra Examples

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

Step 1

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

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Step 1.1

Move the negative in front of the fraction.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

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

Step 1.4.2

Multiply $4$ by $3$ .

$- \frac{3 x \cdot 3}{12} + \frac{x - 4}{3} \cdot \frac{4}{4} = \frac{- 5}{3}$

Step 1.4.3

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

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

Step 1.4.4

Multiply $3$ by $4$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $3$ by $- 3$ .

$\frac{- 9 x + (x - 4) \cdot 4}{12} = \frac{- 5}{3}$

Step 1.6.2

Apply the distributive property.

$\frac{- 9 x + x \cdot 4 - 4 \cdot 4}{12} = \frac{- 5}{3}$

Step 1.6.3

Move $4$ to the left of $x$ .

$\frac{- 9 x + 4 \cdot x - 4 \cdot 4}{12} = \frac{- 5}{3}$

Step 1.6.4

Multiply $- 4$ by $4$ .

$\frac{- 9 x + 4 \cdot x - 16}{12} = \frac{- 5}{3}$

Step 1.6.5

Add $- 9 x$ and $4 x$ .

$\frac{- 5 x - 16}{12} = \frac{- 5}{3}$

Step 1.7

Simplify with factoring out.

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Step 1.7.1

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) - 16}{12} = \frac{- 5}{3}$

Step 1.7.2

Rewrite $- 16$ as $- 1 (16)$ .

$\frac{- (5 x) - 1 (16)}{12} = \frac{- 5}{3}$

Step 1.7.3

Factor $- 1$ out of $- (5 x) - 1 (16)$ .

$\frac{- (5 x + 16)}{12} = \frac{- 5}{3}$

Step 1.7.4

Simplify the expression.

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Step 1.7.4.1

Rewrite $- (5 x + 16)$ as $- 1 (5 x + 16)$ .

$\frac{- 1 (5 x + 16)}{12} = \frac{- 5}{3}$

Step 1.7.4.2

Move the negative in front of the fraction.

$- \frac{5 x + 16}{12} = \frac{- 5}{3}$

Step 2

Move the negative in front of the fraction.

$- \frac{5 x + 16}{12} = - \frac{5}{3}$

Step 3

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{5 x + 16}{12}) = - 12 (- \frac{5}{3})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 12 (- \frac{5 x + 16}{12})$ .

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Step 4.1.1.1

Cancel the common factor of $12$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{5 x + 16}{12}$ into the numerator.

$- 12 \frac{- (5 x + 16)}{12} = - 12 (- \frac{5}{3})$

Step 4.1.1.1.2

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- (5 x + 16)}{12} = - 12 (- \frac{5}{3})$

Step 4.1.1.1.3

Cancel the common factor.

$12 \cdot - 1 \frac{- (5 x + 16)}{12} = - 12 (- \frac{5}{3})$

Step 4.1.1.1.4

Rewrite the expression.

$- - (5 x + 16) = - 12 (- \frac{5}{3})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (5 x + 16) = - 12 (- \frac{5}{3})$

Step 4.1.1.2.2

Multiply $5 x + 16$ by $1$ .

$5 x + 16 = - 12 (- \frac{5}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 12 (- \frac{5}{3})$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$5 x + 16 = - 12 (\frac{- 5}{3})$

Step 4.2.1.1.2

Factor $3$ out of $- 12$ .

$5 x + 16 = 3 (- 4) \frac{- 5}{3}$

Step 4.2.1.1.3

Cancel the common factor.

$5 x + 16 = 3 \cdot - 4 \frac{- 5}{3}$

Step 4.2.1.1.4

Rewrite the expression.

$5 x + 16 = - 4 \cdot - 5$

Step 4.2.1.2

Multiply $- 4$ by $- 5$ .

$5 x + 16 = 20$

Step 5

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

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Step 5.1

Subtract $16$ from both sides of the equation.

$5 x = 20 - 16$

Step 5.2

Subtract $16$ from $20$ .

$5 x = 4$

Step 6

Divide each term in $5 x = 4$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}$

Decimal Form:

$x = 0.8$