Solve for x 2(x-1)+4x=3(x-1)+7

$2 (x - 1) + 4 x = 3 (x - 1) + 7$

Step 1

Simplify $2 (x - 1) + 4 x$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 1 + 4 x = 3 (x - 1) + 7$

Multiply $2$ by $- 1$ .

$2 x - 2 + 4 x = 3 (x - 1) + 7$

Add $2 x$ and $4 x$ .

$6 x - 2 = 3 (x - 1) + 7$

Step 2

Simplify $3 (x - 1) + 7$ .

Simplify each term.

Apply the distributive property.

$6 x - 2 = 3 x + 3 \cdot - 1 + 7$

Multiply $3$ by $- 1$ .

$6 x - 2 = 3 x - 3 + 7$

Add $- 3$ and $7$ .

$6 x - 2 = 3 x + 4$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$6 x - 2 - 3 x = 4$

Subtract $3 x$ from $6 x$ .

$3 x - 2 = 4$

Step 4

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

Add $2$ to both sides of the equation.

$3 x = 4 + 2$

Add $4$ and $2$ .

$3 x = 6$

Step 5

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$