Pre-Algebra Examples

$\frac{1}{7} \cdot (14 x - 11) - 3 x = \frac{3}{7}$

Step 1

Simplify $\frac{1}{7} \cdot (14 x - 11) - 3 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{7} (14 x) + \frac{1}{7} \cdot - 11 - 3 x = \frac{3}{7}$

Step 1.1.2

Cancel the common factor of $7$ .

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Step 1.1.2.1

Factor $7$ out of $14 x$ .

$\frac{1}{7} (7 (2 x)) + \frac{1}{7} \cdot - 11 - 3 x = \frac{3}{7}$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 (2 x)) + \frac{1}{7} \cdot - 11 - 3 x = \frac{3}{7}$

Step 1.1.2.3

Rewrite the expression.

$2 x + \frac{1}{7} \cdot - 11 - 3 x = \frac{3}{7}$

Step 1.1.3

Combine $\frac{1}{7}$ and $- 11$ .

$2 x + \frac{- 11}{7} - 3 x = \frac{3}{7}$

Step 1.1.4

Move the negative in front of the fraction.

$2 x - \frac{11}{7} - 3 x = \frac{3}{7}$

Step 1.2

Subtract $3 x$ from $2 x$ .

$- x - \frac{11}{7} = \frac{3}{7}$

Step 2

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

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Step 2.1

Add $\frac{11}{7}$ to both sides of the equation.

$- x = \frac{3}{7} + \frac{11}{7}$

Step 2.2

Combine the numerators over the common denominator.

$- x = \frac{3 + 11}{7}$

Step 2.3

Add $3$ and $11$ .

$- x = \frac{14}{7}$

Step 2.4

Divide $14$ by $7$ .

$- x = 2$

Step 3

Divide each term in $- x = 2$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $2$ by $- 1$ .

$x = - 2$