Solve the Inequality for x (x-1)/3<=(2x-6)/2

$\frac{x - 1}{3} \leq \frac{2 x - 6}{2}$

Multiply both sides by $3$ .

$\frac{x - 1}{3} \cdot 3 \leq \frac{2 x - 6}{2} \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x - 1}{3} \cdot 3 \leq \frac{2 x - 6}{2} \cdot 3$

Rewrite the expression.

$x - 1 \leq \frac{2 x - 6}{2} \cdot 3$

Simplify the right side.

Simplify $\frac{2 x - 6}{2} \cdot 3$ .

Factor $2$ out of $2 x - 6$ .

Factor $2$ out of $2 x$ .

$x - 1 \leq \frac{2 (x) - 6}{2} \cdot 3$

Factor $2$ out of $- 6$ .

$x - 1 \leq \frac{2 x + 2 \cdot - 3}{2} \cdot 3$

Factor $2$ out of $2 x + 2 \cdot - 3$ .

$x - 1 \leq \frac{2 (x - 3)}{2} \cdot 3$

Cancel the common factor of $2$ .

Cancel the common factor.

$x - 1 \leq \frac{2 (x - 3)}{2} \cdot 3$

Divide $x - 3$ by $1$ .

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

Apply the distributive property.

$x - 1 \leq x \cdot 3 - 3 \cdot 3$

Simplify the expression.

Move $3$ to the left of $x$ .

$x - 1 \leq 3 \cdot x - 3 \cdot 3$

Multiply $- 3$ by $3$ .

$x - 1 \leq 3 x - 9$

Solve for $x$ .

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

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

$x - 1 - 3 x \leq - 9$

Subtract $3 x$ from $x$ .

$- 2 x - 1 \leq - 9$

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

Add $1$ to both sides of the inequality.

$- 2 x \leq - 9 + 1$

Add $- 9$ and $1$ .

$- 2 x \leq - 8$

Divide each term in $- 2 x \leq - 8$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq - 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{- 8}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$x \geq 4$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 4$

Interval Notation:

$[4, \infty)$

Solve the Inequality for x (x-1)/3<=(2x-6)/2

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