Algebra Examples

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

Step 1

Simplify $\frac{2}{3} \cdot (x - (1 - \frac{x - 2}{3})) + 1$ .

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Step 1.1

Simplify terms.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Simplify each term.

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Step 1.1.1.1.1

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

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

Step 1.1.1.1.2

Combine the numerators over the common denominator.

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

Step 1.1.1.1.3

Simplify the numerator.

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Step 1.1.1.1.3.1

Apply the distributive property.

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

Step 1.1.1.1.3.2

Multiply $- 1$ by $- 2$ .

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

Step 1.1.1.1.3.3

Add $3$ and $2$ .

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

Step 1.1.1.2

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

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

Step 1.1.1.3

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

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

Step 1.1.1.4

Combine the numerators over the common denominator.

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

Step 1.1.1.5

Simplify the numerator.

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Step 1.1.1.5.1

Move $3$ to the left of $x$ .

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

Step 1.1.1.5.2

Apply the distributive property.

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

Step 1.1.1.5.3

Multiply $- - x$ .

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Step 1.1.1.5.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.1.1.5.3.2

Multiply $x$ by $1$ .

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

Step 1.1.1.5.4

Multiply $- 1$ by $5$ .

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

Step 1.1.1.5.5

Add $3 x$ and $x$ .

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

Step 1.1.1.6

Multiply $\frac{2}{3} \cdot \frac{4 x - 5}{3}$ .

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Step 1.1.1.6.1

Multiply $\frac{2}{3}$ by $\frac{4 x - 5}{3}$ .

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

Step 1.1.1.6.2

Multiply $3$ by $3$ .

$\frac{2 (4 x - 5)}{9} + 1 = x$

Step 1.1.2

Combine into one fraction.

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Step 1.1.2.1

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

$\frac{2 (4 x - 5)}{9} + \frac{9}{9} = x$

Step 1.1.2.2

Combine the numerators over the common denominator.

$\frac{2 (4 x - 5) + 9}{9} = x$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Apply the distributive property.

$\frac{2 (4 x) + 2 \cdot - 5 + 9}{9} = x$

Step 1.2.2

Multiply $4$ by $2$ .

$\frac{8 x + 2 \cdot - 5 + 9}{9} = x$

Step 1.2.3

Multiply $2$ by $- 5$ .

$\frac{8 x - 10 + 9}{9} = x$

Step 1.2.4

Add $- 10$ and $9$ .

$\frac{8 x - 1}{9} = x$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{8 x - 1}{9} - x = 0$

Step 2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{8 x - 1}{9} - x \cdot \frac{9}{9} = 0$

Step 2.3

Combine $- x$ and $\frac{9}{9}$ .

$\frac{8 x - 1}{9} + \frac{- x \cdot 9}{9} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{8 x - 1 - x \cdot 9}{9} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $9$ by $- 1$ .

$\frac{8 x - 1 - 9 x}{9} = 0$

Step 2.5.2

Subtract $9 x$ from $8 x$ .

$\frac{- x - 1}{9} = 0$

Step 2.6

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

$\frac{- (x) - 1}{9} = 0$

Step 2.7

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

$\frac{- (x) - 1 (1)}{9} = 0$

Step 2.8

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

$\frac{- (x + 1)}{9} = 0$

Step 2.9

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

$\frac{- 1 (x + 1)}{9} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{x + 1}{9} = 0$

Step 3

Set the numerator equal to zero.

$x + 1 = 0$

Step 4

Subtract $1$ from both sides of the equation.

$x = - 1$