Algebra Examples

$2 (- 3 (x - 1) + 5) - 2 (3 x - 5) = 2 (1 - 2 x)$

Step 1

Simplify $2 (- 3 (x - 1) + 5) - 2 (3 x - 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Multiply $- 3$ by $- 1$ .

$2 (- 3 x + 3 + 5) - 2 (3 x - 5) = 2 (1 - 2 x)$

Step 1.1.2

Add $3$ and $5$ .

$2 (- 3 x + 8) - 2 (3 x - 5) = 2 (1 - 2 x)$

Step 1.1.3

Apply the distributive property.

$2 (- 3 x) + 2 \cdot 8 - 2 (3 x - 5) = 2 (1 - 2 x)$

Step 1.1.4

Multiply $- 3$ by $2$ .

$- 6 x + 2 \cdot 8 - 2 (3 x - 5) = 2 (1 - 2 x)$

Step 1.1.5

Multiply $2$ by $8$ .

$- 6 x + 16 - 2 (3 x - 5) = 2 (1 - 2 x)$

Step 1.1.6

Apply the distributive property.

$- 6 x + 16 - 2 (3 x) - 2 \cdot - 5 = 2 (1 - 2 x)$

Step 1.1.7

Multiply $3$ by $- 2$ .

$- 6 x + 16 - 6 x - 2 \cdot - 5 = 2 (1 - 2 x)$

Step 1.1.8

Multiply $- 2$ by $- 5$ .

$- 6 x + 16 - 6 x + 10 = 2 (1 - 2 x)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $6 x$ from $- 6 x$ .

$- 12 x + 16 + 10 = 2 (1 - 2 x)$

Step 1.2.2

Add $16$ and $10$ .

$- 12 x + 26 = 2 (1 - 2 x)$

Step 2

Simplify $2 (1 - 2 x)$ .

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Step 2.1

Apply the distributive property.

$- 12 x + 26 = 2 \cdot 1 + 2 (- 2 x)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $1$ .

$- 12 x + 26 = 2 + 2 (- 2 x)$

Step 2.2.2

Multiply $- 2$ by $2$ .

$- 12 x + 26 = 2 - 4 x$

Step 3

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

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Step 3.1

Add $4 x$ to both sides of the equation.

$- 12 x + 26 + 4 x = 2$

Step 3.2

Add $- 12 x$ and $4 x$ .

$- 8 x + 26 = 2$

Step 4

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

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Step 4.1

Subtract $26$ from both sides of the equation.

$- 8 x = 2 - 26$

Step 4.2

Subtract $26$ from $2$ .

$- 8 x = - 24$

Step 5

Divide each term in $- 8 x = - 24$ by $- 8$ and simplify.

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Step 5.1

Divide each term in $- 8 x = - 24$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 24}{- 8}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 8$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 24}{- 8}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 24}{- 8}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 24$ by $- 8$ .

$x = 3$