Pre-Algebra Examples

$\frac{16 + x}{- 4} = \frac{3 x - 4}{3} + 1$

Step 1

Multiply both sides by $- 4$ .

$\frac{16 + x}{- 4} \cdot - 4 = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{16 + x}{- 4} \cdot - 4$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1.1.1

Factor $4$ out of $- 4$ .

$\frac{16 + x}{4 (- 1)} \cdot - 4 = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.1.2

Factor $4$ out of $- 4$ .

$\frac{16 + x}{4 \cdot - 1} \cdot (4 \cdot - 1) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.1.3

Cancel the common factor.

$\frac{16 + x}{4 \cdot - 1} \cdot (4 \cdot - 1) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.1.4

Rewrite the expression.

$\frac{16 + x}{- 1} \cdot - 1 = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.2

Combine $\frac{16 + x}{- 1}$ and $- 1$ .

$\frac{(16 + x) \cdot - 1}{- 1} = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.3

Simplify the expression.

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Step 2.1.1.1.3.1

Move the negative one from the denominator of $\frac{(16 + x) \cdot - 1}{- 1}$ .

$- 1 \cdot ((16 + x) \cdot - 1) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.3.2

Rewrite $- 1 \cdot ((16 + x) \cdot - 1)$ as $- ((16 + x) \cdot - 1)$ .

$- ((16 + x) \cdot - 1) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.4

Apply the distributive property.

$- (16 \cdot - 1 + x \cdot - 1) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.5

Simplify the expression.

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Step 2.1.1.1.5.1

Multiply $16$ by $- 1$ .

$- (- 16 + x \cdot - 1) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.1.5.2

Move $- 1$ to the left of $x$ .

$- (- 16 - 1 \cdot x) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.2

Rewrite $- 1 x$ as $- x$ .

$- (- 16 - x) = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.3

Simplify by multiplying through.

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Step 2.1.1.3.1

Apply the distributive property.

$- - 16 - - x = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.3.2

Multiply $- 1$ by $- 16$ .

$16 - - x = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.4

Multiply $- - x$ .

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$16 + 1 x = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.4.2

Multiply $x$ by $1$ .

$16 + x = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.1.1.5

Reorder $16$ and $x$ .

$x + 16 = (\frac{3 x - 4}{3} + 1) \cdot - 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{3 x - 4}{3} + 1) \cdot - 4$ .

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Step 2.2.1.1

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

$x + 16 = (\frac{3 x - 4}{3} + \frac{3}{3}) \cdot - 4$

Step 2.2.1.2

Combine the numerators over the common denominator.

$x + 16 = \frac{3 x - 4 + 3}{3} \cdot - 4$

Step 2.2.1.3

Add $- 4$ and $3$ .

$x + 16 = \frac{3 x - 1}{3} \cdot - 4$

Step 2.2.1.4

Combine $\frac{3 x - 1}{3}$ and $- 4$ .

$x + 16 = \frac{(3 x - 1) \cdot - 4}{3}$

Step 2.2.1.5

Simplify the expression.

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Step 2.2.1.5.1

Move $- 4$ to the left of $3 x - 1$ .

$x + 16 = \frac{- 4 \cdot (3 x - 1)}{3}$

Step 2.2.1.5.2

Move the negative in front of the fraction.

$x + 16 = - \frac{4 (3 x - 1)}{3}$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $3$ .

$(x + 16) \cdot 3 = - \frac{4 (3 x - 1)}{3} \cdot 3$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $(x + 16) \cdot 3$ .

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Step 3.2.1.1.1

Apply the distributive property.

$x \cdot 3 + 16 \cdot 3 = - \frac{4 (3 x - 1)}{3} \cdot 3$

Step 3.2.1.1.2

Simplify the expression.

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Step 3.2.1.1.2.1

Move $3$ to the left of $x$ .

$3 \cdot x + 16 \cdot 3 = - \frac{4 (3 x - 1)}{3} \cdot 3$

Step 3.2.1.1.2.2

Multiply $16$ by $3$ .

$3 x + 48 = - \frac{4 (3 x - 1)}{3} \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $- \frac{4 (3 x - 1)}{3} \cdot 3$ .

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Step 3.2.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1.1

Move the leading negative in $- \frac{4 (3 x - 1)}{3}$ into the numerator.

$3 x + 48 = \frac{- 4 (3 x - 1)}{3} \cdot 3$

Step 3.2.2.1.1.2

Cancel the common factor.

$3 x + 48 = \frac{- 4 (3 x - 1)}{3} \cdot 3$

Step 3.2.2.1.1.3

Rewrite the expression.

$3 x + 48 = - 4 (3 x - 1)$

Step 3.2.2.1.2

Apply the distributive property.

$3 x + 48 = - 4 (3 x) - 4 \cdot - 1$

Step 3.2.2.1.3

Multiply.

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Step 3.2.2.1.3.1

Multiply $3$ by $- 4$ .

$3 x + 48 = - 12 x - 4 \cdot - 1$

Step 3.2.2.1.3.2

Multiply $- 4$ by $- 1$ .

$3 x + 48 = - 12 x + 4$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $12 x$ to both sides of the equation.

$3 x + 48 + 12 x = 4$

Step 3.3.1.2

Add $3 x$ and $12 x$ .

$15 x + 48 = 4$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $48$ from both sides of the equation.

$15 x = 4 - 48$

Step 3.3.2.2

Subtract $48$ from $4$ .

$15 x = - 44$

Step 3.3.3

Divide each term in $15 x = - 44$ by $15$ and simplify.

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Step 3.3.3.1

Divide each term in $15 x = - 44$ by $15$ .

$\frac{15 x}{15} = \frac{- 44}{15}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $15$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{15 x}{15} = \frac{- 44}{15}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 44}{15}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Move the negative in front of the fraction.

$x = - \frac{44}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{44}{15}$

Decimal Form:

$x = - 2.9\overline{3}$

Mixed Number Form:

$x = - 2 \frac{14}{15}$