Algebra Examples

$\frac{x}{4} + 16 - 2 (x - 1) = 4$

Step 1

Simplify $\frac{x}{4} + 16 - 2 (x - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{x}{4} + 16 - 2 x - 2 \cdot - 1 = 4$

Step 1.1.2

Multiply $- 2$ by $- 1$ .

$\frac{x}{4} + 16 - 2 x + 2 = 4$

Step 1.2

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

$\frac{x}{4} - 2 x \cdot \frac{4}{4} + 16 + 2 = 4$

Step 1.3

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

$\frac{x}{4} + \frac{- 2 x \cdot 4}{4} + 16 + 2 = 4$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x - 2 x \cdot 4}{4} + 16 + 2 = 4$

Step 1.5

Find the common denominator.

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Step 1.5.1

Write $16$ as a fraction with denominator $1$ .

$\frac{x - 2 x \cdot 4}{4} + \frac{16}{1} + 2 = 4$

Step 1.5.2

Multiply $\frac{16}{1}$ by $\frac{4}{4}$ .

$\frac{x - 2 x \cdot 4}{4} + \frac{16}{1} \cdot \frac{4}{4} + 2 = 4$

Step 1.5.3

Multiply $\frac{16}{1}$ by $\frac{4}{4}$ .

$\frac{x - 2 x \cdot 4}{4} + \frac{16 \cdot 4}{4} + 2 = 4$

Step 1.5.4

Write $2$ as a fraction with denominator $1$ .

$\frac{x - 2 x \cdot 4}{4} + \frac{16 \cdot 4}{4} + \frac{2}{1} = 4$

Step 1.5.5

Multiply $\frac{2}{1}$ by $\frac{4}{4}$ .

$\frac{x - 2 x \cdot 4}{4} + \frac{16 \cdot 4}{4} + \frac{2}{1} \cdot \frac{4}{4} = 4$

Step 1.5.6

Multiply $\frac{2}{1}$ by $\frac{4}{4}$ .

$\frac{x - 2 x \cdot 4}{4} + \frac{16 \cdot 4}{4} + \frac{2 \cdot 4}{4} = 4$

Step 1.6

Combine the numerators over the common denominator.

$\frac{x - 2 x \cdot 4 + 16 \cdot 4 + 2 \cdot 4}{4} = 4$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $4$ by $- 2$ .

$\frac{x - 8 x + 16 \cdot 4 + 2 \cdot 4}{4} = 4$

Step 1.7.2

Multiply $16$ by $4$ .

$\frac{x - 8 x + 64 + 2 \cdot 4}{4} = 4$

Step 1.7.3

Multiply $2$ by $4$ .

$\frac{x - 8 x + 64 + 8}{4} = 4$

Step 1.8

Simplify terms.

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Step 1.8.1

Subtract $8 x$ from $x$ .

$\frac{- 7 x + 64 + 8}{4} = 4$

Step 1.8.2

Add $64$ and $8$ .

$\frac{- 7 x + 72}{4} = 4$

Step 1.8.3

Factor $- 1$ out of $- 7 x$ .

$\frac{- (7 x) + 72}{4} = 4$

Step 1.8.4

Rewrite $72$ as $- 1 (- 72)$ .

$\frac{- (7 x) - 1 (- 72)}{4} = 4$

Step 1.8.5

Factor $- 1$ out of $- (7 x) - 1 (- 72)$ .

$\frac{- (7 x - 72)}{4} = 4$

Step 1.8.6

Simplify the expression.

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Step 1.8.6.1

Rewrite $- (7 x - 72)$ as $- 1 (7 x - 72)$ .

$\frac{- 1 (7 x - 72)}{4} = 4$

Step 1.8.6.2

Move the negative in front of the fraction.

$- \frac{7 x - 72}{4} = 4$

Step 2

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{7 x - 72}{4}) = - 4 \cdot 4$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 4 (- \frac{7 x - 72}{4})$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{7 x - 72}{4}$ into the numerator.

$- 4 \frac{- (7 x - 72)}{4} = - 4 \cdot 4$

Step 3.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- (7 x - 72)}{4} = - 4 \cdot 4$

Step 3.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- (7 x - 72)}{4} = - 4 \cdot 4$

Step 3.1.1.1.4

Rewrite the expression.

$- - (7 x - 72) = - 4 \cdot 4$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (7 x - 72) = - 4 \cdot 4$

Step 3.1.1.2.2

Multiply $7 x - 72$ by $1$ .

$7 x - 72 = - 4 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 4$ by $4$ .

$7 x - 72 = - 16$

Step 4

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

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Step 4.1

Add $72$ to both sides of the equation.

$7 x = - 16 + 72$

Step 4.2

Add $- 16$ and $72$ .

$7 x = 56$

Step 5

Divide each term in $7 x = 56$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 x = 56$ by $7$ .

$\frac{7 x}{7} = \frac{56}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{56}{7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{56}{7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $56$ by $7$ .

$x = 8$