Solve the Inequality for x -3(x+4)-2>=2x+6

$- 3 (x + 4) - 2 \geq 2 x + 6$

Simplify $- 3 (x + 4) - 2$ .

Simplify each term.

Apply the distributive property.

$- 3 x - 3 \cdot 4 - 2 \geq 2 x + 6$

Multiply $- 3$ by $4$ .

$- 3 x - 12 - 2 \geq 2 x + 6$

Subtract $2$ from $- 12$ .

$- 3 x - 14 \geq 2 x + 6$

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

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

$- 3 x - 14 - 2 x \geq 6$

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

$- 5 x - 14 \geq 6$

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

Add $14$ to both sides of the inequality.

$- 5 x \geq 6 + 14$

Add $6$ and $14$ .

$- 5 x \geq 20$

Divide each term in $- 5 x \geq 20$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq 20$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{20}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{20}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{20}{- 5}$

Simplify the right side.

Divide $20$ by $- 5$ .

$x \leq - 4$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 4$

Interval Notation:

$(- \infty, - 4]$

Solve the Inequality for x -3(x+4)-2>=2x+6

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