Solve the Inequality for x x-3>3(x-1)

$x - 3 > 3 (x - 1)$

Step 1

Simplify $3 (x - 1)$ .

Rewrite.

$x - 3 > 0 + 0 + 3 (x - 1)$

Simplify by adding zeros.

$x - 3 > 3 (x - 1)$

Apply the distributive property.

$x - 3 > 3 x + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$x - 3 > 3 x - 3$

Step 2

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

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

$x - 3 - 3 x > - 3$

Subtract $3 x$ from $x$ .

$- 2 x - 3 > - 3$

Step 3

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

Add $3$ to both sides of the inequality.

$- 2 x > - 3 + 3$

Add $- 3$ and $3$ .

$- 2 x > 0$

Step 4

Divide each term in $- 2 x > 0$ by $- 2$ and simplify.

Divide each term in $- 2 x > 0$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{0}{- 2}$

Divide $x$ by $1$ .

$x < \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$x < 0$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 0$

Interval Notation:

$(- \infty, 0)$

Solve the Inequality for x x-3>3(x-1)

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