Solve for x 3(x+6)-2(x+2)>=10

$3 (x + 6) - 2 (x + 2) \geq 10$

Step 1

Simplify $3 (x + 6) - 2 (x + 2)$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 6 - 2 (x + 2) \geq 10$

Multiply $3$ by $6$ .

$3 x + 18 - 2 (x + 2) \geq 10$

Apply the distributive property.

$3 x + 18 - 2 x - 2 \cdot 2 \geq 10$

Multiply $- 2$ by $2$ .

$3 x + 18 - 2 x - 4 \geq 10$

Simplify by adding terms.

Subtract $2 x$ from $3 x$ .

$x + 18 - 4 \geq 10$

Subtract $4$ from $18$ .

$x + 14 \geq 10$

Step 2

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

Subtract $14$ from both sides of the inequality.

$x \geq 10 - 14$

Subtract $14$ from $10$ .

$x \geq - 4$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 4$

Interval Notation:

$[- 4, \infty)$