Solve for w 4(w+1)-7=3(w-1)+w

$4 (w + 1) - 7 = 3 (w - 1) + w$

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

$3 (w - 1) + w = 4 (w + 1) - 7$

Simplify $3 (w - 1) + w$ .

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

$3 w - 3 + w = 4 (w + 1) - 7$

Add $3 w$ and $w$ .

$4 w - 3 = 4 (w + 1) - 7$

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

Simplify each term.

Apply the distributive property.

$4 w - 3 = 4 w + 4 \cdot 1 - 7$

Multiply $4$ by $1$ .

$4 w - 3 = 4 w + 4 - 7$

Subtract $7$ from $4$ .

$4 w - 3 = 4 w - 3$

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

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

$4 w - 3 - 4 w = - 3$

Combine the opposite terms in $4 w - 3 - 4 w$ .

Subtract $4 w$ from $4 w$ .

$0 - 3 = - 3$

Subtract $3$ from $0$ .

$- 3 = - 3$

Since $- 3 = - 3$ , the equation will always be true for any value of $w$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$