Solve the Inequality for x 33+4x<=-(x+7)

$33 + 4 x \leq - (x + 7)$

Step 1

Simplify $- (x + 7)$ .

Rewrite.

$33 + 4 x \leq 0 + 0 - (x + 7)$

Simplify by adding zeros.

$33 + 4 x \leq - (x + 7)$

Apply the distributive property.

$33 + 4 x \leq - x - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$33 + 4 x \leq - x - 7$

Step 2

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

Add $x$ to both sides of the inequality.

$33 + 4 x + x \leq - 7$

Add $4 x$ and $x$ .

$33 + 5 x \leq - 7$

Step 3

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

Subtract $33$ from both sides of the inequality.

$5 x \leq - 7 - 33$

Subtract $33$ from $- 7$ .

$5 x \leq - 40$

Step 4

Divide each term in $5 x \leq - 40$ by $5$ and simplify.

Divide each term in $5 x \leq - 40$ by $5$ .

$\frac{5 x}{5} \leq \frac{- 40}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \leq \frac{- 40}{5}$

Divide $x$ by $1$ .

$x \leq \frac{- 40}{5}$

Simplify the right side.

Divide $- 40$ by $5$ .

$x \leq - 8$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 8$

Interval Notation:

$(- \infty, - 8]$