Solve the Inequality for x 4-6(x+2)>2(x-5)+2

$4 - 6 (x + 2) > 2 (x - 5) + 2$

Simplify $4 - 6 (x + 2)$ .

Simplify each term.

Apply the distributive property.

$4 - 6 x - 6 \cdot 2 > 2 (x - 5) + 2$

Multiply $- 6$ by $2$ .

$4 - 6 x - 12 > 2 (x - 5) + 2$

Subtract $12$ from $4$ .

$- 6 x - 8 > 2 (x - 5) + 2$

Simplify $2 (x - 5) + 2$ .

Simplify each term.

Apply the distributive property.

$- 6 x - 8 > 2 x + 2 \cdot - 5 + 2$

Multiply $2$ by $- 5$ .

$- 6 x - 8 > 2 x - 10 + 2$

Add $- 10$ and $2$ .

$- 6 x - 8 > 2 x - 8$

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

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

$- 6 x - 8 - 2 x > - 8$

Subtract $2 x$ from $- 6 x$ .

$- 8 x - 8 > - 8$

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

Add $8$ to both sides of the inequality.

$- 8 x > - 8 + 8$

Add $- 8$ and $8$ .

$- 8 x > 0$

Divide each term in $- 8 x > 0$ by $- 8$ and simplify.

Divide each term in $- 8 x > 0$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} < \frac{0}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} < \frac{0}{- 8}$

Divide $x$ by $1$ .

$x < \frac{0}{- 8}$

Simplify the right side.

Divide $0$ by $- 8$ .

$x < 0$

The result can be shown in multiple forms.

Inequality Form:

$x < 0$

Interval Notation:

$(- \infty, 0)$

Solve the Inequality for x 4-6(x+2)>2(x-5)+2

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