Algebra Examples

$\frac{4}{10} x - 4 x + \frac{6}{5} = \frac{4}{5}$

Step 1

Simplify $\frac{4}{10} x - 4 x + \frac{6}{5}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $4$ and $10$ .

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Step 1.1.1.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{10} x - 4 x + \frac{6}{5} = \frac{4}{5}$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $2$ out of $10$ .

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

Step 1.1.1.2.2

Cancel the common factor.

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

Step 1.1.1.2.3

Rewrite the expression.

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

Step 1.1.2

Combine $\frac{2}{5}$ and $x$ .

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

Step 1.2

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

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

Step 1.3

Combine $- 4 x$ and $\frac{5}{5}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Multiply $5$ by $- 4$ .

$\frac{2 x - 20 x + 6}{5} = \frac{4}{5}$

Step 1.7

Subtract $20 x$ from $2 x$ .

$\frac{- 18 x + 6}{5} = \frac{4}{5}$

Step 1.8

Factor $6$ out of $- 18 x + 6$ .

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Step 1.8.1

Factor $6$ out of $- 18 x$ .

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

Step 1.8.2

Factor $6$ out of $6$ .

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

Step 1.8.3

Factor $6$ out of $6 (- 3 x) + 6 (1)$ .

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

Step 1.9

Factor $- 1$ out of $- 3 x$ .

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

Step 1.10

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

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

Step 1.11

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

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

Step 1.12

Simplify the expression.

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Step 1.12.1

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

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

Step 1.12.2

Move the negative in front of the fraction.

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

Step 2

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

$- 6 (3 x - 1) = 4$

Step 3

Divide each term in $- 6 (3 x - 1) = 4$ by $- 6$ and simplify.

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Step 3.1

Divide each term in $- 6 (3 x - 1) = 4$ by $- 6$ .

$\frac{- 6 (3 x - 1)}{- 6} = \frac{4}{- 6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 6 (3 x - 1)}{- 6} = \frac{4}{- 6}$

Step 3.2.1.2

Divide $3 x - 1$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $4$ and $- 6$ .

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Step 3.3.1.1

Factor $2$ out of $4$ .

$3 x - 1 = \frac{2 (2)}{- 6}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $- 6$ .

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

Step 3.3.1.2.2

Cancel the common factor.

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

Step 3.3.1.2.3

Rewrite the expression.

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

Step 3.3.2

Move the negative in front of the fraction.

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

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

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

Step 4.2

Write $1$ as a fraction with a common denominator.

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

Step 4.3

Combine the numerators over the common denominator.

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

Step 4.4

Add $- 2$ and $3$ .

$3 x = \frac{1}{3}$

Step 5

Divide each term in $3 x = \frac{1}{3}$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 x = \frac{1}{3}$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{1}{3}}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{1}{3}}{3}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{3}}{3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{3} \cdot \frac{1}{3}$

Step 5.3.2

Multiply $\frac{1}{3} \cdot \frac{1}{3}$ .

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Step 5.3.2.1

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

$x = \frac{1}{3 \cdot 3}$

Step 5.3.2.2

Multiply $3$ by $3$ .

$x = \frac{1}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{9}$

Decimal Form:

$x = 0.\overline{1}$