Algebra Examples

$2 x + 5 (- \frac{4}{7}) = 2$

Step 1

Simplify each term.

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Step 1.1

Multiply $5 (- \frac{4}{7})$ .

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Step 1.1.1

Multiply $- 1$ by $5$ .

$2 x - 5 (\frac{4}{7}) = 2$

Step 1.1.2

Combine $- 5$ and $\frac{4}{7}$ .

$2 x + \frac{- 5 \cdot 4}{7} = 2$

Step 1.1.3

Multiply $- 5$ by $4$ .

$2 x + \frac{- 20}{7} = 2$

Step 1.2

Move the negative in front of the fraction.

$2 x - \frac{20}{7} = 2$

Step 2

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

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Step 2.1

Add $\frac{20}{7}$ to both sides of the equation.

$2 x = 2 + \frac{20}{7}$

Step 2.2

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

$2 x = 2 \cdot \frac{7}{7} + \frac{20}{7}$

Step 2.3

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

$2 x = \frac{2 \cdot 7}{7} + \frac{20}{7}$

Step 2.4

Combine the numerators over the common denominator.

$2 x = \frac{2 \cdot 7 + 20}{7}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $7$ .

$2 x = \frac{14 + 20}{7}$

Step 2.5.2

Add $14$ and $20$ .

$2 x = \frac{34}{7}$

Step 3

Divide each term in $2 x = \frac{34}{7}$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x = \frac{34}{7}$ by $2$ .

$\frac{2 x}{2} = \frac{\frac{34}{7}}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{34}{7}}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{34}{7}}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{34}{7} \cdot \frac{1}{2}$

Step 3.3.2

Cancel the common factor of $2$ .

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Step 3.3.2.1

Factor $2$ out of $34$ .

$x = \frac{2 (17)}{7} \cdot \frac{1}{2}$

Step 3.3.2.2

Cancel the common factor.

$x = \frac{2 \cdot 17}{7} \cdot \frac{1}{2}$

Step 3.3.2.3

Rewrite the expression.

$x = \frac{17}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{7}$

Decimal Form:

$x = 2.\overline{428571}$

Mixed Number Form:

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