Solve for x 4(x-1)+7=5(2x-3)

$4 (x - 1) + 7 = 5 (2 x - 3)$

Step 1

Simplify $4 (x - 1) + 7$ .

Simplify each term.

Apply the distributive property.

$4 x + 4 \cdot - 1 + 7 = 5 (2 x - 3)$

Multiply $4$ by $- 1$ .

$4 x - 4 + 7 = 5 (2 x - 3)$

Add $- 4$ and $7$ .

$4 x + 3 = 5 (2 x - 3)$

Step 2

Simplify $5 (2 x - 3)$ .

Apply the distributive property.

$4 x + 3 = 5 (2 x) + 5 \cdot - 3$

Multiply.

Multiply $2$ by $5$ .

$4 x + 3 = 10 x + 5 \cdot - 3$

Multiply $5$ by $- 3$ .

$4 x + 3 = 10 x - 15$

Step 3

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

Subtract $10 x$ from both sides of the equation.

$4 x + 3 - 10 x = - 15$

Subtract $10 x$ from $4 x$ .

$- 6 x + 3 = - 15$

Step 4

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

Subtract $3$ from both sides of the equation.

$- 6 x = - 15 - 3$

Subtract $3$ from $- 15$ .

$- 6 x = - 18$

Step 5

Divide each term in $- 6 x = - 18$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 18$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 18}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 18}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 6}$

Simplify the right side.

Divide $- 18$ by $- 6$ .

$x = 3$