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

$3 (x - 1) < - 3 (2 - 2 x)$

Step 1

Simplify $3 (x - 1)$ .

Rewrite.

$0 + 0 + 3 (x - 1) < - 3 (2 - 2 x)$

Simplify by adding zeros.

$3 (x - 1) < - 3 (2 - 2 x)$

Apply the distributive property.

$3 x + 3 \cdot - 1 < - 3 (2 - 2 x)$

Multiply $3$ by $- 1$ .

$3 x - 3 < - 3 (2 - 2 x)$

Step 2

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

Apply the distributive property.

$3 x - 3 < - 3 \cdot 2 - 3 (- 2 x)$

Multiply.

Multiply $- 3$ by $2$ .

$3 x - 3 < - 6 - 3 (- 2 x)$

Multiply $- 2$ by $- 3$ .

$3 x - 3 < - 6 + 6 x$

Step 3

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

Subtract $6 x$ from both sides of the inequality.

$3 x - 3 - 6 x < - 6$

Subtract $6 x$ from $3 x$ .

$- 3 x - 3 < - 6$

Step 4

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

Add $3$ to both sides of the inequality.

$- 3 x < - 6 + 3$

Add $- 6$ and $3$ .

$- 3 x < - 3$

Step 5

Divide each term in $- 3 x < - 3$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 3$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{- 3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{- 3}{- 3}$

Divide $x$ by $1$ .

$x > \frac{- 3}{- 3}$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x > 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$

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

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