Algebra Examples

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

Step 1

Simplify $\frac{2}{5} \cdot (4 x - 3) - 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $\frac{2}{5} (4 x)$ .

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Step 1.1.2.1

Combine $4$ and $\frac{2}{5}$ .

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

Step 1.1.2.2

Multiply $4$ by $2$ .

$\frac{8}{5} x + \frac{2}{5} \cdot - 3 - 2 x = \frac{4}{5} - x$

Step 1.1.2.3

Combine $\frac{8}{5}$ and $x$ .

$\frac{8 x}{5} + \frac{2}{5} \cdot - 3 - 2 x = \frac{4}{5} - x$

Step 1.1.3

Multiply $\frac{2}{5} \cdot - 3$ .

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Step 1.1.3.1

Combine $\frac{2}{5}$ and $- 3$ .

$\frac{8 x}{5} + \frac{2 \cdot - 3}{5} - 2 x = \frac{4}{5} - x$

Step 1.1.3.2

Multiply $2$ by $- 3$ .

$\frac{8 x}{5} + \frac{- 6}{5} - 2 x = \frac{4}{5} - x$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{8 x}{5} - \frac{6}{5} - 2 x = \frac{4}{5} - x$

Step 1.2

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

$\frac{8 x}{5} - 2 x \cdot \frac{5}{5} - \frac{6}{5} = \frac{4}{5} - x$

Step 1.3

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

$\frac{8 x}{5} + \frac{- 2 x \cdot 5}{5} - \frac{6}{5} = \frac{4}{5} - x$

Step 1.4

Combine the numerators over the common denominator.

$\frac{8 x - 2 x \cdot 5}{5} - \frac{6}{5} = \frac{4}{5} - x$

Step 1.5

Combine the numerators over the common denominator.

$\frac{8 x - 2 x \cdot 5 - 6}{5} = \frac{4}{5} - x$

Step 1.6

Multiply $5$ by $- 2$ .

$\frac{8 x - 10 x - 6}{5} = \frac{4}{5} - x$

Step 1.7

Subtract $10 x$ from $8 x$ .

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

Step 1.8

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

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Step 1.8.1

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

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

Step 1.8.2

Factor $2$ out of $- 6$ .

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

Step 1.8.3

Factor $2$ out of $2 (- x) + 2 (- 3)$ .

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

Step 1.9

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

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

Step 1.10

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

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

Step 1.11

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

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

Step 1.12

Simplify the expression.

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Step 1.12.1

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

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

Step 1.12.2

Move the negative in front of the fraction.

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

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Add $x$ to both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

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

Step 2.5.2

Multiply $- 2$ by $3$ .

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

Step 2.5.3

Move $5$ to the left of $x$ .

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

Step 2.5.4

Add $- 2 x$ and $5 x$ .

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

Step 2.5.5

Factor $3$ out of $3 x - 6$ .

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Step 2.5.5.1

Factor $3$ out of $3 x$ .

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

Step 2.5.5.2

Factor $3$ out of $- 6$ .

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

Step 2.5.5.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

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

Step 3

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

$3 (x - 2) = 4$

Step 4

Divide each term in $3 (x - 2) = 4$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 (x - 2) = 4$ by $3$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x - 2$ by $1$ .

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

Step 5

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

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Step 5.1

Add $2$ to both sides of the equation.

$x = \frac{4}{3} + 2$

Step 5.2

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

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

Step 5.3

Combine $2$ and $\frac{3}{3}$ .

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

Step 5.4

Combine the numerators over the common denominator.

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

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $2$ by $3$ .

$x = \frac{4 + 6}{3}$

Step 5.5.2

Add $4$ and $6$ .

$x = \frac{10}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{3}$

Decimal Form:

$x = 3.\overline{3}$

Mixed Number Form:

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