Solve the Inequality for x 2(3x-7)>=-x

$2 (3 x - 7) \geq - x$

Step 1

Simplify $2 (3 x - 7)$ .

Start simplifying.

$0 + 0 + 2 (3 x - 7) \geq - x$

Simplify by adding zeros.

$2 (3 x - 7) \geq - x$

Apply the distributive property.

$2 (3 x) + 2 \cdot - 7 \geq - x$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 7 \geq - x$

Multiply $2$ by $- 7$ .

$6 x - 14 \geq - x$

Step 2

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

Add $x$ to both sides of the inequality.

$6 x - 14 + x \geq 0$

Add $6 x$ and $x$ .

$7 x - 14 \geq 0$

Step 3

Add $14$ to both sides of the inequality.

$7 x \geq 14$

Step 4

Divide each term in $7 x \geq 14$ by $7$ and simplify.

Divide each term in $7 x \geq 14$ by $7$ .

$\frac{7 x}{7} \geq \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} \geq \frac{14}{7}$

Divide $x$ by $1$ .

$x \geq \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$x \geq 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$