Algebra Examples

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

Step 1

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

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Step 1.1

Combine $\frac{5}{6}$ and $x$ .

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

Step 1.2

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

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

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $- 2 x$ and $\frac{6}{6}$ .

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

Step 1.3.2

Combine the numerators over the common denominator.

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

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $x$ out of $5 x - 2 x \cdot 6$ .

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Step 1.4.1.1.1

Factor $x$ out of $5 x$ .

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

Step 1.4.1.1.2

Factor $x$ out of $- 2 x \cdot 6$ .

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

Step 1.4.1.1.3

Factor $x$ out of $x \cdot 5 + x (- 2 \cdot 6)$ .

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

Step 1.4.1.2

Multiply $- 2$ by $6$ .

$\frac{x (5 - 12)}{6} + \frac{4}{3} = \frac{5}{3}$

Step 1.4.1.3

Subtract $12$ from $5$ .

$\frac{x \cdot - 7}{6} + \frac{4}{3} = \frac{5}{3}$

Step 1.4.2

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{6} + \frac{4}{3} = \frac{5}{3}$

Step 1.4.3

Move the negative in front of the fraction.

$- \frac{7 x}{6} + \frac{4}{3} = \frac{5}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{4}{3}$ from both sides of the equation.

$- \frac{7 x}{6} = \frac{5}{3} - \frac{4}{3}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{7 x}{6} = \frac{5 - 4}{3}$

Step 2.3

Subtract $4$ from $5$ .

$- \frac{7 x}{6} = \frac{1}{3}$

Step 3

Multiply both sides of the equation by $- \frac{6}{7}$ .

$- \frac{6}{7} (- \frac{7 x}{6}) = - \frac{6}{7} \cdot \frac{1}{3}$

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 $- \frac{6}{7} (- \frac{7 x}{6})$ .

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Step 4.1.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$\frac{- 6}{7} (- \frac{7 x}{6}) = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{7 x}{6}$ into the numerator.

$\frac{- 6}{7} \cdot \frac{- 7 x}{6} = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.1.3

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{7} \cdot \frac{- 7 x}{6} = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{6 \cdot - 1}{7} \cdot \frac{- 7 x}{6} = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{6}{7} \cdot \frac{1}{3}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{6}{7} \cdot \frac{1}{3}$ .

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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 $- \frac{6}{7}$ into the numerator.

$x = \frac{- 6}{7} \cdot \frac{1}{3}$

Step 4.2.1.1.2

Factor $3$ out of $- 6$ .

$x = \frac{3 (- 2)}{7} \cdot \frac{1}{3}$

Step 4.2.1.1.3

Cancel the common factor.

$x = \frac{3 \cdot - 2}{7} \cdot \frac{1}{3}$

Step 4.2.1.1.4

Rewrite the expression.

$x = \frac{- 2}{7}$

Step 4.2.1.2

Move the negative in front of the fraction.

$x = - \frac{2}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{7}$

Decimal Form:

$x = - 0.\overline{285714}$