Solve the Inequality for x -(3x+3)-2x>-4(x-2)-2

$- (3 x + 3) - 2 x > - 4 (x - 2) - 2$

Step 1

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

Simplify each term.

Apply the distributive property.

$- (3 x) - 1 \cdot 3 - 2 x > - 4 (x - 2) - 2$

Multiply $3$ by $- 1$ .

$- 3 x - 1 \cdot 3 - 2 x > - 4 (x - 2) - 2$

Multiply $- 1$ by $3$ .

$- 3 x - 3 - 2 x > - 4 (x - 2) - 2$

Subtract $2 x$ from $- 3 x$ .

$- 5 x - 3 > - 4 (x - 2) - 2$

Step 2

Simplify $- 4 (x - 2) - 2$ .

Simplify each term.

Apply the distributive property.

$- 5 x - 3 > - 4 x - 4 \cdot - 2 - 2$

Multiply $- 4$ by $- 2$ .

$- 5 x - 3 > - 4 x + 8 - 2$

Subtract $2$ from $8$ .

$- 5 x - 3 > - 4 x + 6$

Step 3

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

Add $4 x$ to both sides of the inequality.

$- 5 x - 3 + 4 x > 6$

Add $- 5 x$ and $4 x$ .

$- x - 3 > 6$

Step 4

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

Add $3$ to both sides of the inequality.

$- x > 6 + 3$

Add $6$ and $3$ .

$- x > 9$

Step 5

Divide each term in $- x > 9$ by $- 1$ and simplify.

Divide each term in $- x > 9$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{9}{- 1}$

Divide $x$ by $1$ .

$x < \frac{9}{- 1}$

Simplify the right side.

Divide $9$ by $- 1$ .

$x < - 9$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - 9$

Interval Notation:

$(- \infty, - 9)$

Solve the Inequality for x -(3x+3)-2x>-4(x-2)-2

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