Algebra Examples

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

Step 1

Simplify $2 x + 4 (3 - 2 x)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $4$ by $3$ .

$2 x + 12 + 4 (- 2 x) = \frac{3 (2 x + 2)}{6} + 4$

Step 1.1.3

Multiply $- 2$ by $4$ .

$2 x + 12 - 8 x = \frac{3 (2 x + 2)}{6} + 4$

Step 1.2

Subtract $8 x$ from $2 x$ .

$- 6 x + 12 = \frac{3 (2 x + 2)}{6} + 4$

Step 2

Simplify $\frac{3 (2 x + 2)}{6} + 4$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Cancel the common factors.

Tap for more steps...

Step 2.1.1.1

Factor $3$ out of $6$ .

$- 6 x + 12 = \frac{3 (2 x + 2)}{3 \cdot 2} + 4$

Step 2.1.1.2

Cancel the common factor.

$- 6 x + 12 = \frac{3 (2 x + 2)}{3 \cdot 2} + 4$

Step 2.1.1.3

Rewrite the expression.

$- 6 x + 12 = \frac{2 x + 2}{2} + 4$

Step 2.1.2

Cancel the common factor of $2 x + 2$ and $2$ .

Tap for more steps...

Step 2.1.2.1

Factor $2$ out of $2 x$ .

$- 6 x + 12 = \frac{2 (x) + 2}{2} + 4$

Step 2.1.2.2

Factor $2$ out of $2$ .

$- 6 x + 12 = \frac{2 (x) + 2 \cdot 1}{2} + 4$

Step 2.1.2.3

Factor $2$ out of $2 (x) + 2 (1)$ .

$- 6 x + 12 = \frac{2 (x + 1)}{2} + 4$

Step 2.1.2.4

Cancel the common factors.

Tap for more steps...

Step 2.1.2.4.1

Factor $2$ out of $2$ .

$- 6 x + 12 = \frac{2 (x + 1)}{2 (1)} + 4$

Step 2.1.2.4.2

Cancel the common factor.

$- 6 x + 12 = \frac{2 (x + 1)}{2 \cdot 1} + 4$

Step 2.1.2.4.3

Rewrite the expression.

$- 6 x + 12 = \frac{x + 1}{1} + 4$

Step 2.1.2.4.4

Divide $x + 1$ by $1$ .

$- 6 x + 12 = x + 1 + 4$

Step 2.2

Add $1$ and $4$ .

$- 6 x + 12 = x + 5$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $x$ from both sides of the equation.

$- 6 x + 12 - x = 5$

Step 3.2

Subtract $x$ from $- 6 x$ .

$- 7 x + 12 = 5$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $12$ from both sides of the equation.

$- 7 x = 5 - 12$

Step 4.2

Subtract $12$ from $5$ .

$- 7 x = - 7$

Step 5

Divide each term in $- 7 x = - 7$ by $- 7$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 7 x = - 7$ by $- 7$ .

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

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 7$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $- 7$ by $- 7$ .

$x = 1$