Algebra Examples

$2 (x - 1) + 3 = x - 3 (x + 1)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x - 3 (x + 1) = 2 (x - 1) + 3$

Step 2

Simplify $x - 3 (x + 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $- 3$ by $1$ .

$x - 3 x - 3 = 2 (x - 1) + 3$

Step 2.2

Subtract $3 x$ from $x$ .

$- 2 x - 3 = 2 (x - 1) + 3$

Step 3

Simplify $2 (x - 1) + 3$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 2 x - 3 = 2 x + 2 \cdot - 1 + 3$

Step 3.1.2

Multiply $2$ by $- 1$ .

$- 2 x - 3 = 2 x - 2 + 3$

Step 3.2

Add $- 2$ and $3$ .

$- 2 x - 3 = 2 x + 1$

Step 4

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

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Step 4.1

Subtract $2 x$ from both sides of the equation.

$- 2 x - 3 - 2 x = 1$

Step 4.2

Subtract $2 x$ from $- 2 x$ .

$- 4 x - 3 = 1$

Step 5

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

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Step 5.1

Add $3$ to both sides of the equation.

$- 4 x = 1 + 3$

Step 5.2

Add $1$ and $3$ .

$- 4 x = 4$

Step 6

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

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Step 6.1

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

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 4$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $4$ by $- 4$ .

$x = - 1$