Solve the Inequality for x -2x+3(-4x+6)<=116

$- 2 x + 3 (- 4 x + 6) \leq 116$

Step 1

Simplify $- 2 x + 3 (- 4 x + 6)$ .

Simplify each term.

Apply the distributive property.

$- 2 x + 3 (- 4 x) + 3 \cdot 6 \leq 116$

Multiply $- 4$ by $3$ .

$- 2 x - 12 x + 3 \cdot 6 \leq 116$

Multiply $3$ by $6$ .

$- 2 x - 12 x + 18 \leq 116$

Subtract $12 x$ from $- 2 x$ .

$- 14 x + 18 \leq 116$

Step 2

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

Subtract $18$ from both sides of the inequality.

$- 14 x \leq 116 - 18$

Subtract $18$ from $116$ .

$- 14 x \leq 98$

Step 3

Divide each term in $- 14 x \leq 98$ by $- 14$ and simplify.

Divide each term in $- 14 x \leq 98$ by $- 14$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 14 x}{- 14} \geq \frac{98}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 x}{- 14} \geq \frac{98}{- 14}$

Divide $x$ by $1$ .

$x \geq \frac{98}{- 14}$

Simplify the right side.

Divide $98$ by $- 14$ .

$x \geq - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 7$

Interval Notation:

$[- 7, \infty)$

Solve the Inequality for x -2x+3(-4x+6)<=116

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