Algebra Examples

$\frac{3 x}{7} - 1 = 6 + \frac{x}{2}$

Step 1

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

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Step 1.1

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

$\frac{3 x}{7} - 1 - \frac{x}{2} = 6$

Step 1.2

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

$\frac{3 x}{7} \cdot \frac{2}{2} - \frac{x}{2} - 1 = 6$

Step 1.3

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

$\frac{3 x}{7} \cdot \frac{2}{2} - \frac{x}{2} \cdot \frac{7}{7} - 1 = 6$

Step 1.4

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

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Step 1.4.1

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

$\frac{3 x \cdot 2}{7 \cdot 2} - \frac{x}{2} \cdot \frac{7}{7} - 1 = 6$

Step 1.4.2

Multiply $7$ by $2$ .

$\frac{3 x \cdot 2}{14} - \frac{x}{2} \cdot \frac{7}{7} - 1 = 6$

Step 1.4.3

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

$\frac{3 x \cdot 2}{14} - \frac{x \cdot 7}{2 \cdot 7} - 1 = 6$

Step 1.4.4

Multiply $2$ by $7$ .

$\frac{3 x \cdot 2}{14} - \frac{x \cdot 7}{14} - 1 = 6$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - x \cdot 7}{14} - 1 = 6$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $x$ out of $3 x \cdot 2 - x \cdot 7$ .

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Step 1.6.1.1.1

Factor $x$ out of $3 x \cdot 2$ .

$\frac{x (3 \cdot 2) - x \cdot 7}{14} - 1 = 6$

Step 1.6.1.1.2

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

$\frac{x (3 \cdot 2) + x (- 1 \cdot 7)}{14} - 1 = 6$

Step 1.6.1.1.3

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

$\frac{x (3 \cdot 2 - 1 \cdot 7)}{14} - 1 = 6$

Step 1.6.1.2

Multiply $3$ by $2$ .

$\frac{x (6 - 1 \cdot 7)}{14} - 1 = 6$

Step 1.6.1.3

Multiply $- 1$ by $7$ .

$\frac{x (6 - 7)}{14} - 1 = 6$

Step 1.6.1.4

Subtract $7$ from $6$ .

$\frac{x \cdot - 1}{14} - 1 = 6$

Step 1.6.2

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{14} - 1 = 6$

Step 1.6.3

Move the negative in front of the fraction.

$- \frac{x}{14} - 1 = 6$

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$- \frac{x}{14} = 6 + 1$

Step 2.2

Add $6$ and $1$ .

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

Step 3

Multiply both sides of the equation by $- 14$ .

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

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 $- 14 (- \frac{x}{14})$ .

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Step 4.1.1.1

Cancel the common factor of $14$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{x}{14}$ into the numerator.

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

Step 4.1.1.1.2

Factor $14$ out of $- 14$ .

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

Step 4.1.1.1.3

Cancel the common factor.

$14 \cdot - 1 \frac{- x}{14} = - 14 \cdot 7$

Step 4.1.1.1.4

Rewrite the expression.

$- - x = - 14 \cdot 7$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 14 \cdot 7$

Step 4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 14 \cdot 7$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 14$ by $7$ .

$x = - 98$