Solve the Inequality for x -20+x>=-7(2x+5)

$- 20 + x \geq - 7 (2 x + 5)$

Simplify $- 7 (2 x + 5)$ .

Rewrite.

$- 20 + x \geq 0 + 0 - 7 (2 x + 5)$

Simplify by adding zeros.

$- 20 + x \geq - 7 (2 x + 5)$

Apply the distributive property.

$- 20 + x \geq - 7 (2 x) - 7 \cdot 5$

Multiply.

Multiply $2$ by $- 7$ .

$- 20 + x \geq - 14 x - 7 \cdot 5$

Multiply $- 7$ by $5$ .

$- 20 + x \geq - 14 x - 35$

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

Add $14 x$ to both sides of the inequality.

$- 20 + x + 14 x \geq - 35$

Add $x$ and $14 x$ .

$- 20 + 15 x \geq - 35$

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

Add $20$ to both sides of the inequality.

$15 x \geq - 35 + 20$

Add $- 35$ and $20$ .

$15 x \geq - 15$

Divide each term in $15 x \geq - 15$ by $15$ and simplify.

Divide each term in $15 x \geq - 15$ by $15$ .

$\frac{15 x}{15} \geq \frac{- 15}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 x}{15} \geq \frac{- 15}{15}$

Divide $x$ by $1$ .

$x \geq \frac{- 15}{15}$

Simplify the right side.

Divide $- 15$ by $15$ .

$x \geq - 1$

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 1$

Interval Notation:

$[- 1, \infty)$