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

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

Simplify $5 x + 2 (2 - x)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Multiply $- 1$ by $2$ .

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

Subtract $2 x$ from $5 x$ .

$3 x + 4 = 3 (1 + x) + 1$

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

Simplify each term.

Apply the distributive property.

$3 x + 4 = 3 \cdot 1 + 3 x + 1$

Multiply $3$ by $1$ .

$3 x + 4 = 3 + 3 x + 1$

Add $3$ and $1$ .

$3 x + 4 = 3 x + 4$

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

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

$3 x + 4 - 3 x = 4$

Combine the opposite terms in $3 x + 4 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 + 4 = 4$

Add $0$ and $4$ .

$4 = 4$

Since $4 = 4$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$