Algebra Examples

$x = \frac{2 x^{2} + x - 7}{2 x + 8}$

Step 1

Factor $2$ out of $2 x + 8$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$x = \frac{2 x^{2} + x - 7}{2 (x) + 8}$

Step 1.2

Factor $2$ out of $8$ .

$x = \frac{2 x^{2} + x - 7}{2 x + 2 \cdot 4}$

Step 1.3

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

$x = \frac{2 x^{2} + x - 7}{2 (x + 4)}$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, 2 (x + 4)$

Step 2.2

The LCM of one and any expression is the expression.

$2 (x + 4)$

Step 3

Multiply each term in $x = \frac{2 x^{2} + x - 7}{2 (x + 4)}$ by $2 (x + 4)$ to eliminate the fractions.

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Step 3.1

Multiply each term in $x = \frac{2 x^{2} + x - 7}{2 (x + 4)}$ by $2 (x + 4)$ .

$x (2 (x + 4)) = \frac{2 x^{2} + x - 7}{2 (x + 4)} (2 (x + 4))$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 x (x + 4) = \frac{2 x^{2} + x - 7}{2 (x + 4)} (2 (x + 4))$

Step 3.2.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 4 = \frac{2 x^{2} + x - 7}{2 (x + 4)} (2 (x + 4))$

Step 3.2.3

Multiply $x$ by $x$ by adding the exponents.

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Step 3.2.3.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 4 = \frac{2 x^{2} + x - 7}{2 (x + 4)} (2 (x + 4))$

Step 3.2.3.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 4 = \frac{2 x^{2} + x - 7}{2 (x + 4)} (2 (x + 4))$

Step 3.2.4

Multiply $4$ by $2$ .

$2 x^{2} + 8 x = \frac{2 x^{2} + x - 7}{2 (x + 4)} (2 (x + 4))$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite using the commutative property of multiplication.

$2 x^{2} + 8 x = 2 \frac{2 x^{2} + x - 7}{2 (x + 4)} (x + 4)$

Step 3.3.2

Cancel the common factor of $2$ .

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Step 3.3.2.1

Cancel the common factor.

$2 x^{2} + 8 x = 2 \frac{2 x^{2} + x - 7}{2 (x + 4)} (x + 4)$

Step 3.3.2.2

Rewrite the expression.

$2 x^{2} + 8 x = \frac{2 x^{2} + x - 7}{x + 4} (x + 4)$

Step 3.3.3

Cancel the common factor of $x + 4$ .

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Step 3.3.3.1

Cancel the common factor.

$2 x^{2} + 8 x = \frac{2 x^{2} + x - 7}{x + 4} (x + 4)$

Step 3.3.3.2

Rewrite the expression.

$2 x^{2} + 8 x = 2 x^{2} + x - 7$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

Subtract $2 x^{2}$ from both sides of the equation.

$2 x^{2} + 8 x - 2 x^{2} = x - 7$

Step 4.1.2

Subtract $x$ from both sides of the equation.

$2 x^{2} + 8 x - 2 x^{2} - x = - 7$

Step 4.1.3

Combine the opposite terms in $2 x^{2} + 8 x - 2 x^{2} - x$ .

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Step 4.1.3.1

Subtract $2 x^{2}$ from $2 x^{2}$ .

$8 x + 0 - x = - 7$

Step 4.1.3.2

Add $8 x$ and $0$ .

$8 x - x = - 7$

Step 4.1.4

Subtract $x$ from $8 x$ .

$7 x = - 7$

Step 4.2

Divide each term in $7 x = - 7$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 x = - 7$ by $7$ .

$\frac{7 x}{7} = \frac{- 7}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 7}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 7$ by $7$ .

$x = - 1$