Solve for x -3-6(4x+6)>-111

$- 3 - 6 (4 x + 6) > - 111$

Step 1

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

Simplify each term.

Apply the distributive property.

$- 3 - 6 (4 x) - 6 \cdot 6 > - 111$

Multiply $4$ by $- 6$ .

$- 3 - 24 x - 6 \cdot 6 > - 111$

Multiply $- 6$ by $6$ .

$- 3 - 24 x - 36 > - 111$

Subtract $36$ from $- 3$ .

$- 24 x - 39 > - 111$

Step 2

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

Add $39$ to both sides of the inequality.

$- 24 x > - 111 + 39$

Add $- 111$ and $39$ .

$- 24 x > - 72$

Step 3

Divide each term in $- 24 x > - 72$ by $- 24$ and simplify.

Divide each term in $- 24 x > - 72$ by $- 24$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 24 x}{- 24} < \frac{- 72}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} < \frac{- 72}{- 24}$

Divide $x$ by $1$ .

$x < \frac{- 72}{- 24}$

Simplify the right side.

Divide $- 72$ by $- 24$ .

$x < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 3$

Interval Notation:

$(- \infty, 3)$

Solve for x -3-6(4x+6)>-111

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