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

$4 - 3 (1 - x) \leq 3$

Step 1

Simplify $4 - 3 (1 - x)$ .

Simplify each term.

Apply the distributive property.

$4 - 3 \cdot 1 - 3 (- x) \leq 3$

Multiply $- 3$ by $1$ .

$4 - 3 - 3 (- x) \leq 3$

Multiply $- 1$ by $- 3$ .

$4 - 3 + 3 x \leq 3$

Subtract $3$ from $4$ .

$1 + 3 x \leq 3$

Step 2

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

Subtract $1$ from both sides of the inequality.

$3 x \leq 3 - 1$

Subtract $1$ from $3$ .

$3 x \leq 2$

Step 3

Divide each term in $3 x \leq 2$ by $3$ and simplify.

Divide each term in $3 x \leq 2$ by $3$ .

$\frac{3 x}{3} \leq \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{2}{3}$

Divide $x$ by $1$ .

$x \leq \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{2}{3}$

Interval Notation:

$(- \infty, \frac{2}{3}]$