Pre-Algebra Examples

$21 - \frac{1}{28} \cdot (3 x) = 14 - \frac{1}{28} \cdot (2 x)$

Step 1

Simplify each term.

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Step 1.1

Multiply $- \frac{1}{28} (3 x)$ .

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Step 1.1.1

Multiply $3$ by $- 1$ .

$21 - 3 (\frac{1}{28}) x = 14 - \frac{1}{28} \cdot (2 x)$

Step 1.1.2

Combine $- 3$ and $\frac{1}{28}$ .

$21 + \frac{- 3}{28} x = 14 - \frac{1}{28} \cdot (2 x)$

Step 1.1.3

Combine $\frac{- 3}{28}$ and $x$ .

$21 + \frac{- 3 x}{28} = 14 - \frac{1}{28} \cdot (2 x)$

Step 1.2

Move the negative in front of the fraction.

$21 - \frac{3 x}{28} = 14 - \frac{1}{28} \cdot (2 x)$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Move the leading negative in $- \frac{1}{28}$ into the numerator.

$21 - \frac{3 x}{28} = 14 + \frac{- 1}{28} \cdot (2 x)$

Step 2.1.2

Factor $2$ out of $28$ .

$21 - \frac{3 x}{28} = 14 + \frac{- 1}{2 (14)} \cdot (2 x)$

Step 2.1.3

Factor $2$ out of $2 x$ .

$21 - \frac{3 x}{28} = 14 + \frac{- 1}{2 (14)} \cdot (2 (x))$

Step 2.1.4

Cancel the common factor.

$21 - \frac{3 x}{28} = 14 + \frac{- 1}{2 \cdot 14} \cdot (2 x)$

Step 2.1.5

Rewrite the expression.

$21 - \frac{3 x}{28} = 14 + \frac{- 1}{14} \cdot x$

Step 2.2

Combine $\frac{- 1}{14}$ and $x$ .

$21 - \frac{3 x}{28} = 14 + \frac{- x}{14}$

Step 2.3

Move the negative in front of the fraction.

$21 - \frac{3 x}{28} = 14 - \frac{x}{14}$

Step 3

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

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Step 3.1

Add $\frac{x}{14}$ to both sides of the equation.

$21 - \frac{3 x}{28} + \frac{x}{14} = 14$

Step 3.2

To write $\frac{x}{14}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$21 - \frac{3 x}{28} + \frac{x}{14} \cdot \frac{2}{2} = 14$

Step 3.3

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{x}{14}$ by $\frac{2}{2}$ .

$21 - \frac{3 x}{28} + \frac{x \cdot 2}{14 \cdot 2} = 14$

Step 3.3.2

Multiply $14$ by $2$ .

$21 - \frac{3 x}{28} + \frac{x \cdot 2}{28} = 14$

Step 3.4

Combine the numerators over the common denominator.

$21 + \frac{- 3 x + x \cdot 2}{28} = 14$

Step 3.5

Add $- 3 x$ and $x \cdot 2$ .

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Step 3.5.1

Reorder $x$ and $2$ .

$21 + \frac{- 3 x + 2 \cdot x}{28} = 14$

Step 3.5.2

Add $- 3 x$ and $2 \cdot x$ .

$21 + \frac{- x}{28} = 14$

Step 3.6

Move the negative in front of the fraction.

$21 - \frac{x}{28} = 14$

Step 4

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

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Step 4.1

Subtract $21$ from both sides of the equation.

$- \frac{x}{28} = 14 - 21$

Step 4.2

Subtract $21$ from $14$ .

$- \frac{x}{28} = - 7$

Step 5

Multiply both sides of the equation by $- 28$ .

$- 28 (- \frac{x}{28}) = - 28 \cdot - 7$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- 28 (- \frac{x}{28})$ .

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Step 6.1.1.1

Cancel the common factor of $28$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{x}{28}$ into the numerator.

$- 28 \frac{- x}{28} = - 28 \cdot - 7$

Step 6.1.1.1.2

Factor $28$ out of $- 28$ .

$28 (- 1) \frac{- x}{28} = - 28 \cdot - 7$

Step 6.1.1.1.3

Cancel the common factor.

$28 \cdot - 1 \frac{- x}{28} = - 28 \cdot - 7$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 28 \cdot - 7$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 28 \cdot - 7$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 28 \cdot - 7$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 28$ by $- 7$ .

$x = 196$