Solve the Inequality for x 5(x+2)>=3x-4

$5 (x + 2) \geq 3 x - 4$

Step 1

Simplify $5 (x + 2)$ .

Rewrite.

$0 + 0 + 5 (x + 2) \geq 3 x - 4$

Simplify by adding zeros.

$5 (x + 2) \geq 3 x - 4$

Apply the distributive property.

$5 x + 5 \cdot 2 \geq 3 x - 4$

Multiply $5$ by $2$ .

$5 x + 10 \geq 3 x - 4$

Step 2

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

Subtract $3 x$ from both sides of the inequality.

$5 x + 10 - 3 x \geq - 4$

Subtract $3 x$ from $5 x$ .

$2 x + 10 \geq - 4$

Step 3

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

Subtract $10$ from both sides of the inequality.

$2 x \geq - 4 - 10$

Subtract $10$ from $- 4$ .

$2 x \geq - 14$

Step 4

Divide each term in $2 x \geq - 14$ by $2$ and simplify.

Divide each term in $2 x \geq - 14$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 14$ by $2$ .

$x \geq - 7$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 7$

Interval Notation:

$[- 7, \infty)$