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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $4$ by $- 1$ .

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

Subtract $1$ from $- 4$ .

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

Step 2

Simplify $2 (2 x - 3)$ .

Apply the distributive property.

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

Multiply.

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 3$ .

$4 x - 5 = 4 x - 6$

Step 3

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

Subtract $4 x$ from both sides of the equation.

$4 x - 5 - 4 x = - 6$

Combine the opposite terms in $4 x - 5 - 4 x$ .

Subtract $4 x$ from $4 x$ .

$0 - 5 = - 6$

Subtract $5$ from $0$ .

$- 5 = - 6$

Step 4

Since $- 5 \neq - 6$ , there are no solutions.

No solution