Solve the Inequality for x -2(3x-4)-(x+2)>=-15

$- 2 (3 x - 4) - (x + 2) \geq - 15$

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

Simplify each term.

Apply the distributive property.

$- 2 (3 x) - 2 \cdot - 4 - (x + 2) \geq - 15$

Multiply $3$ by $- 2$ .

$- 6 x - 2 \cdot - 4 - (x + 2) \geq - 15$

Multiply $- 2$ by $- 4$ .

$- 6 x + 8 - (x + 2) \geq - 15$

Apply the distributive property.

$- 6 x + 8 - x - 1 \cdot 2 \geq - 15$

Multiply $- 1$ by $2$ .

$- 6 x + 8 - x - 2 \geq - 15$

Simplify by adding terms.

Subtract $x$ from $- 6 x$ .

$- 7 x + 8 - 2 \geq - 15$

Subtract $2$ from $8$ .

$- 7 x + 6 \geq - 15$

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

Subtract $6$ from both sides of the inequality.

$- 7 x \geq - 15 - 6$

Subtract $6$ from $- 15$ .

$- 7 x \geq - 21$

Divide each term in $- 7 x \geq - 21$ by $- 7$ and simplify.

Divide each term in $- 7 x \geq - 21$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} \leq \frac{- 21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} \leq \frac{- 21}{- 7}$

Divide $x$ by $1$ .

$x \leq \frac{- 21}{- 7}$

Simplify the right side.

Divide $- 21$ by $- 7$ .

$x \leq 3$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$

Solve the Inequality for x -2(3x-4)-(x+2)>=-15

Related Questions

Support LCMGCF.com by disabling your adblocker.