Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Subtract $x$ from both sides of the equation.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

Simplify the numerator.

Tap for more steps...

Step 1.5.1.1

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

Tap for more steps...

Step 1.5.1.1.1

Factor $x$ out of $3 x$ .

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

Step 1.5.1.1.2

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

$8 + \frac{x \cdot 3 + x (- 1 \cdot 7)}{7} = 0$

Step 1.5.1.1.3

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

$8 + \frac{x (3 - 1 \cdot 7)}{7} = 0$

Step 1.5.1.2

Multiply $- 1$ by $7$ .

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

Step 1.5.1.3

Subtract $7$ from $3$ .

$8 + \frac{x \cdot - 4}{7} = 0$

Step 1.5.2

Move $- 4$ to the left of $x$ .

$8 + \frac{- 4 \cdot x}{7} = 0$

Step 1.5.3

Move the negative in front of the fraction.

$8 - \frac{4 x}{7} = 0$

Step 2

Subtract $8$ from both sides of the equation.

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

Step 3

Multiply both sides of the equation by $- \frac{7}{4}$ .

$- \frac{7}{4} (- \frac{4 x}{7}) = - \frac{7}{4} \cdot - 8$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

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

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.1.1.1.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$\frac{- 7}{4} (- \frac{4 x}{7}) = - \frac{7}{4} \cdot - 8$

Step 4.1.1.1.2

Move the leading negative in $- \frac{4 x}{7}$ into the numerator.

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

Step 4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{4} \cdot \frac{- 4 x}{7} = - \frac{7}{4} \cdot - 8$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{4} \cdot \frac{- 4 x}{7} = - \frac{7}{4} \cdot - 8$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 x) = - \frac{7}{4} \cdot - 8$

Step 4.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $4$ out of $- 4 x$ .

$\frac{- 1}{4} (4 (- x)) = - \frac{7}{4} \cdot - 8$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- x)) = - \frac{7}{4} \cdot - 8$

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.1.1.3

Multiply.

Tap for more steps...

Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{7}{4} \cdot - 8$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

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

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- \frac{7}{4} \cdot - 8$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.2.1.1.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

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

Step 4.2.1.1.2

Factor $4$ out of $- 8$ .

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

Step 4.2.1.1.3

Cancel the common factor.

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

Step 4.2.1.1.4

Rewrite the expression.

$x = - 7 \cdot - 2$

Step 4.2.1.2

Multiply $- 7$ by $- 2$ .

$x = 14$