Algebra Examples

$14 + \frac{5}{7} x - 20 = 4 (\frac{1}{7} x - 1)$

Step 1

Simplify $14 + \frac{5}{7} x - 20$ .

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Step 1.1

Combine $\frac{5}{7}$ and $x$ .

$14 + \frac{5 x}{7} - 20 = 4 (\frac{1}{7} x - 1)$

Step 1.2

Subtract $20$ from $14$ .

$\frac{5 x}{7} - 6 = 4 (\frac{1}{7} x - 1)$

Step 2

Simplify $4 (\frac{1}{7} x - 1)$ .

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Step 2.1

Combine $\frac{1}{7}$ and $x$ .

$\frac{5 x}{7} - 6 = 4 (\frac{x}{7} - 1)$

Step 2.2

Apply the distributive property.

$\frac{5 x}{7} - 6 = 4 \frac{x}{7} + 4 \cdot - 1$

Step 2.3

Combine $4$ and $\frac{x}{7}$ .

$\frac{5 x}{7} - 6 = \frac{4 x}{7} + 4 \cdot - 1$

Step 2.4

Multiply $4$ by $- 1$ .

$\frac{5 x}{7} - 6 = \frac{4 x}{7} - 4$

Step 3

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

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Step 3.1

Subtract $\frac{4 x}{7}$ from both sides of the equation.

$\frac{5 x}{7} - 6 - \frac{4 x}{7} = - 4$

Step 3.2

Combine the numerators over the common denominator.

$- 6 + \frac{5 x - 4 x}{7} = - 4$

Step 3.3

Subtract $4 x$ from $5 x$ .

$- 6 + \frac{x}{7} = - 4$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$\frac{x}{7} = - 4 + 6$

Step 4.2

Add $- 4$ and $6$ .

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

Step 5

Multiply both sides of the equation by $7$ .

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

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

Cancel the common factor of $7$ .

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Step 6.1.1.1

Cancel the common factor.

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

Step 6.1.1.2

Rewrite the expression.

$x = 7 \cdot 2$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $7$ by $2$ .

$x = 14$