Solve the Inequality for x -2(3x+6)>=4(x+7)

$- 2 (3 x + 6) \geq 4 (x + 7)$

Simplify $- 2 (3 x + 6)$ .

Start simplifying.

$0 + 0 - 2 (3 x + 6) \geq 4 (x + 7)$

Simplify by adding zeros.

$- 2 (3 x + 6) \geq 4 (x + 7)$

Apply the distributive property.

$- 2 (3 x) - 2 \cdot 6 \geq 4 (x + 7)$

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 \cdot 6 \geq 4 (x + 7)$

Multiply $- 2$ by $6$ .

$- 6 x - 12 \geq 4 (x + 7)$

Simplify $4 (x + 7)$ .

Apply the distributive property.

$- 6 x - 12 \geq 4 x + 4 \cdot 7$

Multiply $4$ by $7$ .

$- 6 x - 12 \geq 4 x + 28$

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

Subtract $4 x$ from both sides of the inequality.

$- 6 x - 12 - 4 x \geq 28$

Subtract $4 x$ from $- 6 x$ .

$- 10 x - 12 \geq 28$

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

Add $12$ to both sides of the inequality.

$- 10 x \geq 28 + 12$

Add $28$ and $12$ .

$- 10 x \geq 40$

Divide each term in $- 10 x \geq 40$ by $- 10$ and simplify.

Divide each term in $- 10 x \geq 40$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 x}{- 10} \leq \frac{40}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} \leq \frac{40}{- 10}$

Divide $x$ by $1$ .

$x \leq \frac{40}{- 10}$

Simplify the right side.

Divide $40$ by $- 10$ .

$x \leq - 4$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 4$

Interval Notation:

$(- \infty, - 4]$

Solve the Inequality for x -2(3x+6)>=4(x+7)

Related Questions

Support LCMGCF.com by disabling your adblocker.