Solve the Inequality for x x-(5-3x)<=2x-1

$x - (5 - 3 x) \leq 2 x - 1$

Simplify $x - (5 - 3 x)$ .

Simplify each term.

Apply the distributive property.

$x - 1 \cdot 5 - (- 3 x) \leq 2 x - 1$

Multiply $- 1$ by $5$ .

$x - 5 - (- 3 x) \leq 2 x - 1$

Multiply $- 3$ by $- 1$ .

$x - 5 + 3 x \leq 2 x - 1$

Add $x$ and $3 x$ .

$4 x - 5 \leq 2 x - 1$

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

Subtract $2 x$ from both sides of the inequality.

$4 x - 5 - 2 x \leq - 1$

Subtract $2 x$ from $4 x$ .

$2 x - 5 \leq - 1$

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

Add $5$ to both sides of the inequality.

$2 x \leq - 1 + 5$

Add $- 1$ and $5$ .

$2 x \leq 4$

Divide each term in $2 x \leq 4$ by $2$ and simplify.

Divide each term in $2 x \leq 4$ by $2$ .

$\frac{2 x}{2} \leq \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{4}{2}$

Divide $x$ by $1$ .

$x \leq \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x \leq 2$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2$

Interval Notation:

$(- \infty, 2]$