Algebra Examples

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Apply the distributive property.

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

Step 2.1.1.1.2

Multiply $2$ by $2$ .

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

Step 2.1.1.1.3

Multiply $2$ by $1$ .

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

Step 2.1.1.2

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.1.1.3

Simplify terms.

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Step 2.1.1.3.1

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

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

Step 2.1.1.3.2

Combine the numerators over the common denominator.

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

Step 2.1.1.4

Simplify each term.

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Step 2.1.1.4.1

Simplify the numerator.

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Step 2.1.1.4.1.1

Factor $x$ out of $4 x \cdot 2 - 3 x$ .

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Step 2.1.1.4.1.1.1

Factor $x$ out of $4 x \cdot 2$ .

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

Step 2.1.1.4.1.1.2

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

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

Step 2.1.1.4.1.1.3

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 3$ .

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

Step 2.1.1.4.1.2

Multiply $4$ by $2$ .

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

Step 2.1.1.4.1.3

Subtract $3$ from $8$ .

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

Step 2.1.1.4.2

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

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

Step 2.1.1.5

Simplify terms.

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Step 2.1.1.5.1

Apply the distributive property.

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

Step 2.1.1.5.2

Cancel the common factor of $2$ .

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Step 2.1.1.5.2.1

Cancel the common factor.

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

Step 2.1.1.5.2.2

Rewrite the expression.

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

Step 2.1.1.5.3

Multiply $2$ by $2$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

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

Step 2.2.1.1.2

Rewrite the expression.

$5 x + 4 = - 3 (4 + x)$

Step 2.2.1.2

Apply the distributive property.

$5 x + 4 = - 3 \cdot 4 - 3 x$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $- 3$ by $4$ .

$5 x + 4 = - 12 - 3 x$

Step 2.2.1.3.2

Reorder $- 12$ and $- 3 x$ .

$5 x + 4 = - 3 x - 12$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $3 x$ to both sides of the equation.

$5 x + 4 + 3 x = - 12$

Step 3.1.2

Add $5 x$ and $3 x$ .

$8 x + 4 = - 12$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$8 x = - 12 - 4$

Step 3.2.2

Subtract $4$ from $- 12$ .

$8 x = - 16$

Step 3.3

Divide each term in $8 x = - 16$ by $8$ and simplify.

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Step 3.3.1

Divide each term in $8 x = - 16$ by $8$ .

$\frac{8 x}{8} = \frac{- 16}{8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 16}{8}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 16}{8}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 16$ by $8$ .

$x = - 2$