Calculus Examples

$\frac{x}{6} - 4 = \frac{x}{3} - 3$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $\frac{x}{3}$ from both sides of the equation.

$\frac{x}{6} - 4 - \frac{x}{3} = - 3$

Step 1.2

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

$\frac{x}{6} - \frac{x}{3} \cdot \frac{2}{2} - 4 = - 3$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

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

$\frac{x}{6} - \frac{x \cdot 2}{3 \cdot 2} - 4 = - 3$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{x}{6} - \frac{x \cdot 2}{6} - 4 = - 3$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2}{6} - 4 = - 3$

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 $x - x \cdot 2$ .

Tap for more steps...

Step 1.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 2}{6} - 4 = - 3$

Step 1.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 2}{6} - 4 = - 3$

Step 1.5.1.1.3

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

$\frac{x \cdot 1 + x (- 1 \cdot 2)}{6} - 4 = - 3$

Step 1.5.1.1.4

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

$\frac{x (1 - 1 \cdot 2)}{6} - 4 = - 3$

Step 1.5.1.2

Multiply $- 1$ by $2$ .

$\frac{x (1 - 2)}{6} - 4 = - 3$

Step 1.5.1.3

Subtract $2$ from $1$ .

$\frac{x \cdot - 1}{6} - 4 = - 3$

Step 1.5.2

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

$\frac{- 1 \cdot x}{6} - 4 = - 3$

Step 1.5.3

Move the negative in front of the fraction.

$- \frac{x}{6} - 4 = - 3$

Step 2

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

Tap for more steps...

Step 2.1

Add $4$ to both sides of the equation.

$- \frac{x}{6} = - 3 + 4$

Step 2.2

Add $- 3$ and $4$ .

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

Step 3

Multiply both sides of the equation by $- 6$ .

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

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 $- 6 (- \frac{x}{6})$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 4.1.1.1.1

Move the leading negative in $- \frac{x}{6}$ into the numerator.

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

Step 4.1.1.1.2

Factor $6$ out of $- 6$ .

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

Step 4.1.1.1.3

Cancel the common factor.

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

Step 4.1.1.1.4

Rewrite the expression.

$- - x = - 6 \cdot 1$

Step 4.1.1.2

Multiply.

Tap for more steps...

Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 6 \cdot 1$

Step 4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 6 \cdot 1$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $- 6$ by $1$ .

$x = - 6$