Algebra Examples

$\frac{4}{7} (\frac{21}{8} x + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1

Simplify $\frac{4}{7} \cdot (\frac{21}{8} x + \frac{1}{2})$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{4}{7} \cdot (\frac{21}{8} x + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.2

Simplify by adding zeros.

$\frac{4}{7} \cdot (\frac{21}{8} x + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.3

Combine $\frac{21}{8}$ and $x$ .

$\frac{4}{7} \cdot (\frac{21 x}{8} + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.4

Apply the distributive property.

$\frac{4}{7} \cdot \frac{21 x}{8} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Factor $4$ out of $8$ .

$\frac{4}{7} \cdot \frac{21 x}{4 (2)} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.5.2

Cancel the common factor.

$\frac{4}{7} \cdot \frac{21 x}{4 \cdot 2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.5.3

Rewrite the expression.

$\frac{1}{7} \cdot \frac{21 x}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.6

Cancel the common factor of $7$ .

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Step 1.6.1

Factor $7$ out of $21 x$ .

$\frac{1}{7} \cdot \frac{7 (3 x)}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.6.2

Cancel the common factor.

$\frac{1}{7} \cdot \frac{7 (3 x)}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.6.3

Rewrite the expression.

$\frac{3 x}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Factor $2$ out of $4$ .

$\frac{3 x}{2} + \frac{2 (2)}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.7.2

Cancel the common factor.

$\frac{3 x}{2} + \frac{2 \cdot 2}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1.7.3

Rewrite the expression.

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 2

Simplify $- 2 (\frac{1}{7} - \frac{5}{28} x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $x$ and $\frac{5}{28}$ .

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7} - \frac{x \cdot 5}{28})$

Step 2.1.2

Move $5$ to the left of $x$ .

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7} - \frac{5 x}{28})$

Step 2.2

Simplify terms.

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Step 2.2.1

Apply the distributive property.

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7}) - 2 (- \frac{5 x}{28})$

Step 2.2.2

Combine $- 2$ and $\frac{1}{7}$ .

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} - 2 (- \frac{5 x}{28})$

Step 2.2.3

Cancel the common factor of $2$ .

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Step 2.2.3.1

Move the leading negative in $- \frac{5 x}{28}$ into the numerator.

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} - 2 \frac{- 5 x}{28}$

Step 2.2.3.2

Factor $2$ out of $- 2$ .

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} + 2 (- 1) \frac{- 5 x}{28}$

Step 2.2.3.3

Factor $2$ out of $28$ .

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} + 2 \cdot - 1 \frac{- 5 x}{2 \cdot 14}$

Step 2.2.3.4

Cancel the common factor.

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} + 2 \cdot - 1 \frac{- 5 x}{2 \cdot 14}$

Step 2.2.3.5

Rewrite the expression.

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} - 1 \frac{- 5 x}{14}$

Step 2.3

Simplify each term.

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Step 2.3.1

Move the negative in front of the fraction.

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} - 1 \frac{- 5 x}{14}$

Step 2.3.2

Move the negative in front of the fraction.

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} - 1 (- \frac{5 x}{14})$

Step 2.3.3

Multiply $- 1 (- \frac{5 x}{14})$ .

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Step 2.3.3.1

Multiply $- 1$ by $- 1$ .

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} + 1 \frac{5 x}{14}$

Step 2.3.3.2

Multiply $\frac{5 x}{14}$ by $1$ .

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} + \frac{5 x}{14}$

Step 3

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

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Step 3.1

Subtract $\frac{5 x}{14}$ from both sides of the equation.

$\frac{3 x}{2} + \frac{2}{7} - \frac{5 x}{14} = - \frac{2}{7}$

Step 3.2

To write $\frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 x}{2} \cdot \frac{7}{7} - \frac{5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.3

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{3 x}{2}$ by $\frac{7}{7}$ .

$\frac{3 x \cdot 7}{2 \cdot 7} - \frac{5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.3.2

Multiply $2$ by $7$ .

$\frac{3 x \cdot 7}{14} - \frac{5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 7 - 5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $3 x \cdot 7 - 5 x$ .

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Step 3.5.1.1.1

Factor $x$ out of $3 x \cdot 7$ .

$\frac{x (3 \cdot 7) - 5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.5.1.1.2

Factor $x$ out of $- 5 x$ .

$\frac{x (3 \cdot 7) + x \cdot - 5}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.5.1.1.3

Factor $x$ out of $x (3 \cdot 7) + x \cdot - 5$ .

$\frac{x (3 \cdot 7 - 5)}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.5.1.2

Multiply $3$ by $7$ .

$\frac{x (21 - 5)}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.5.1.3

Subtract $5$ from $21$ .

$\frac{x \cdot 16}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.5.2

Cancel the common factor of $16$ and $14$ .

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Step 3.5.2.1

Factor $2$ out of $x \cdot 16$ .

$\frac{2 (x \cdot 8)}{14} + \frac{2}{7} = - \frac{2}{7}$

Step 3.5.2.2

Cancel the common factors.

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Step 3.5.2.2.1

Factor $2$ out of $14$ .

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

Step 3.5.2.2.2

Cancel the common factor.

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

Step 3.5.2.2.3

Rewrite the expression.

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

Step 3.5.3

Move $8$ to the left of $x$ .

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

Step 4

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

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Step 4.1

Subtract $\frac{2}{7}$ from both sides of the equation.

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

Step 4.2

Combine the numerators over the common denominator.

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

Step 4.3

Subtract $2$ from $- 2$ .

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

Step 4.4

Move the negative in front of the fraction.

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

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$8 x = - 4$

Step 6

Divide each term in $8 x = - 4$ by $8$ and simplify.

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Step 6.1

Divide each term in $8 x = - 4$ by $8$ .

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $8$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $- 4$ and $8$ .

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Step 6.3.1.1

Factor $4$ out of $- 4$ .

$x = \frac{4 (- 1)}{8}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $4$ out of $8$ .

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

Step 6.3.1.2.2

Cancel the common factor.

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

Step 6.3.1.2.3

Rewrite the expression.

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

Step 6.3.2

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$