Algebra Examples

$\frac{6 x}{7} - 3 = 2 x$

Step 1

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

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$\frac{6 x}{7} - 3 - 2 x = 0$

Step 1.2

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

$\frac{6 x}{7} - 2 x \cdot \frac{7}{7} - 3 = 0$

Step 1.3

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

$\frac{6 x}{7} + \frac{- 2 x \cdot 7}{7} - 3 = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{6 x - 2 x \cdot 7}{7} - 3 = 0$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $2 x$ out of $6 x - 2 x \cdot 7$ .

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Step 1.5.1.1.1

Factor $2 x$ out of $6 x$ .

$\frac{2 x (3) - 2 x \cdot 7}{7} - 3 = 0$

Step 1.5.1.1.2

Factor $2 x$ out of $- 2 x \cdot 7$ .

$\frac{2 x (3) + 2 x (- 1 \cdot 7)}{7} - 3 = 0$

Step 1.5.1.1.3

Factor $2 x$ out of $2 x (3) + 2 x (- 1 \cdot 7)$ .

$\frac{2 x (3 - 1 \cdot 7)}{7} - 3 = 0$

Step 1.5.1.2

Multiply $- 1$ by $7$ .

$\frac{2 x (3 - 7)}{7} - 3 = 0$

Step 1.5.1.3

Subtract $7$ from $3$ .

$\frac{2 x \cdot - 4}{7} - 3 = 0$

Step 1.5.1.4

Multiply $- 4$ by $2$ .

$\frac{- 8 x}{7} - 3 = 0$

Step 1.5.2

Move the negative in front of the fraction.

$- \frac{8 x}{7} - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$- \frac{8 x}{7} = 3$

Step 3

Multiply both sides of the equation by $- \frac{7}{8}$ .

$- \frac{7}{8} (- \frac{8 x}{7}) = - \frac{7}{8} \cdot 3$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{7}{8} (- \frac{8 x}{7})$ .

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Step 4.1.1.1

Cancel the common factor of $7$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{7}{8}$ into the numerator.

$\frac{- 7}{8} (- \frac{8 x}{7}) = - \frac{7}{8} \cdot 3$

Step 4.1.1.1.2

Move the leading negative in $- \frac{8 x}{7}$ into the numerator.

$\frac{- 7}{8} \cdot \frac{- 8 x}{7} = - \frac{7}{8} \cdot 3$

Step 4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{8} \cdot \frac{- 8 x}{7} = - \frac{7}{8} \cdot 3$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{8} \cdot \frac{- 8 x}{7} = - \frac{7}{8} \cdot 3$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{8} (- 8 x) = - \frac{7}{8} \cdot 3$

Step 4.1.1.2

Cancel the common factor of $8$ .

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Step 4.1.1.2.1

Factor $8$ out of $- 8 x$ .

$\frac{- 1}{8} (8 (- x)) = - \frac{7}{8} \cdot 3$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{8} (8 (- x)) = - \frac{7}{8} \cdot 3$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{7}{8} \cdot 3$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{7}{8} \cdot 3$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{7}{8} \cdot 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{7}{8} \cdot 3$ .

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Step 4.2.1.1

Multiply $- \frac{7}{8} \cdot 3$ .

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Step 4.2.1.1.1

Multiply $3$ by $- 1$ .

$x = - 3 (\frac{7}{8})$

Step 4.2.1.1.2

Combine $- 3$ and $\frac{7}{8}$ .

$x = \frac{- 3 \cdot 7}{8}$

Step 4.2.1.1.3

Multiply $- 3$ by $7$ .

$x = \frac{- 21}{8}$

Step 4.2.1.2

Move the negative in front of the fraction.

$x = - \frac{21}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{21}{8}$

Decimal Form:

$x = - 2.625$

Mixed Number Form:

$x = - 2 \frac{5}{8}$