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

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

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

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 1 + 1 + 2 x = 4 x - 1$

Multiply $2$ by $- 1$ .

$2 x - 2 + 1 + 2 x = 4 x - 1$

Simplify by adding terms.

Add $2 x$ and $2 x$ .

$4 x - 2 + 1 = 4 x - 1$

Add $- 2$ and $1$ .

$4 x - 1 = 4 x - 1$

Step 3

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

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

$4 x - 1 - 4 x = - 1$

Combine the opposite terms in $4 x - 1 - 4 x$ .

Subtract $4 x$ from $4 x$ .

$0 - 1 = - 1$

Subtract $1$ from $0$ .

$- 1 = - 1$

Step 4

Since $- 1 = - 1$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$