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

$3 - 2 (1 - x) \leq 2$

Step 1

Simplify $3 - 2 (1 - x)$ .

Simplify each term.

Apply the distributive property.

$3 - 2 \cdot 1 - 2 (- x) \leq 2$

Multiply $- 2$ by $1$ .

$3 - 2 - 2 (- x) \leq 2$

Multiply $- 1$ by $- 2$ .

$3 - 2 + 2 x \leq 2$

Subtract $2$ from $3$ .

$1 + 2 x \leq 2$

Step 2

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

Subtract $1$ from both sides of the inequality.

$2 x \leq 2 - 1$

Subtract $1$ from $2$ .

$2 x \leq 1$

Step 3

Divide each term in $2 x \leq 1$ by $2$ and simplify.

Divide each term in $2 x \leq 1$ by $2$ .

$\frac{2 x}{2} \leq \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{1}{2}$

Divide $x$ by $1$ .

$x \leq \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{1}{2}$

Interval Notation:

$(- \infty, \frac{1}{2}]$