Algebra Examples

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

Step 1

Simplify $\frac{3 x - 7}{2} - \frac{x + 2}{3}$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

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

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

Step 1.3.2

Multiply $2$ by $3$ .

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

Step 1.3.3

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

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

Step 1.3.4

Multiply $3$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Multiply $3$ by $3$ .

$\frac{9 x - 7 \cdot 3 - (x + 2) \cdot 2}{6} = x - 6$

Step 1.5.3

Multiply $- 7$ by $3$ .

$\frac{9 x - 21 - (x + 2) \cdot 2}{6} = x - 6$

Step 1.5.4

Apply the distributive property.

$\frac{9 x - 21 + (- x - 1 \cdot 2) \cdot 2}{6} = x - 6$

Step 1.5.5

Multiply $- 1$ by $2$ .

$\frac{9 x - 21 + (- x - 2) \cdot 2}{6} = x - 6$

Step 1.5.6

Apply the distributive property.

$\frac{9 x - 21 - x \cdot 2 - 2 \cdot 2}{6} = x - 6$

Step 1.5.7

Multiply $2$ by $- 1$ .

$\frac{9 x - 21 - 2 x - 2 \cdot 2}{6} = x - 6$

Step 1.5.8

Multiply $- 2$ by $2$ .

$\frac{9 x - 21 - 2 x - 4}{6} = x - 6$

Step 1.5.9

Subtract $2 x$ from $9 x$ .

$\frac{7 x - 21 - 4}{6} = x - 6$

Step 1.5.10

Subtract $4$ from $- 21$ .

$\frac{7 x - 25}{6} = x - 6$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{7 x - 25}{6} - x = - 6$

Step 2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{7 x - 25}{6} - x \cdot \frac{6}{6} = - 6$

Step 2.3

Combine $- x$ and $\frac{6}{6}$ .

$\frac{7 x - 25}{6} + \frac{- x \cdot 6}{6} = - 6$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 x - 25 - x \cdot 6}{6} = - 6$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $6$ by $- 1$ .

$\frac{7 x - 25 - 6 x}{6} = - 6$

Step 2.5.2

Subtract $6 x$ from $7 x$ .

$\frac{x - 25}{6} = - 6$

Step 3

Multiply both sides of the equation by $6$ .

$6 \frac{x - 25}{6} = 6 \cdot - 6$

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

Cancel the common factor of $6$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor.

$6 \frac{x - 25}{6} = 6 \cdot - 6$

Step 4.1.1.2

Rewrite the expression.

$x - 25 = 6 \cdot - 6$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $6$ by $- 6$ .

$x - 25 = - 36$

Step 5

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

Tap for more steps...

Step 5.1

Add $25$ to both sides of the equation.

$x = - 36 + 25$

Step 5.2

Add $- 36$ and $25$ .

$x = - 11$