Solve the Inequality for x (x+2)/2>=-7-x/2

$\frac{x + 2}{2} \geq - 7 - \frac{x}{2}$

Multiply both sides by $2$ .

$\frac{x + 2}{2} \cdot 2 \geq (- 7 - \frac{x}{2}) \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x + 2}{2} \cdot 2 \geq (- 7 - \frac{x}{2}) \cdot 2$

Rewrite the expression.

$x + 2 \geq (- 7 - \frac{x}{2}) \cdot 2$

Simplify the right side.

Simplify $(- 7 - \frac{x}{2}) \cdot 2$ .

Apply the distributive property.

$x + 2 \geq - 7 \cdot 2 - \frac{x}{2} \cdot 2$

Multiply $- 7$ by $2$ .

$x + 2 \geq - 14 - \frac{x}{2} \cdot 2$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$x + 2 \geq - 14 + \frac{- x}{2} \cdot 2$

Cancel the common factor.

$x + 2 \geq - 14 + \frac{- x}{2} \cdot 2$

Rewrite the expression.

$x + 2 \geq - 14 - x$

Reorder $- 14$ and $- x$ .

$x + 2 \geq - x - 14$

Solve for $x$ .

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

Add $x$ to both sides of the inequality.

$x + 2 + x \geq - 14$

Add $x$ and $x$ .

$2 x + 2 \geq - 14$

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

Subtract $2$ from both sides of the inequality.

$2 x \geq - 14 - 2$

Subtract $2$ from $- 14$ .

$2 x \geq - 16$

Divide each term in $2 x \geq - 16$ by $2$ and simplify.

Divide each term in $2 x \geq - 16$ by $2$ .

$\frac{2 x}{2} \geq \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{- 16}{2}$

Divide $x$ by $1$ .

$x \geq \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$x \geq - 8$

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 8$

Interval Notation:

$[- 8, \infty)$

Solve the Inequality for x (x+2)/2>=-7-x/2

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