Solve the Inequality for x 2<=4(x+1)+3x+6

$2 \leq 4 (x + 1) + 3 x + 6$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$4 (x + 1) + 3 x + 6 \geq 2$

Step 2

Simplify $4 (x + 1) + 3 x + 6$ .

Simplify each term.

Apply the distributive property.

$4 x + 4 \cdot 1 + 3 x + 6 \geq 2$

Multiply $4$ by $1$ .

$4 x + 4 + 3 x + 6 \geq 2$

Simplify by adding terms.

Add $4 x$ and $3 x$ .

$7 x + 4 + 6 \geq 2$

Add $4$ and $6$ .

$7 x + 10 \geq 2$

Step 3

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

Subtract $10$ from both sides of the inequality.

$7 x \geq 2 - 10$

Subtract $10$ from $2$ .

$7 x \geq - 8$

Step 4

Divide each term in $7 x \geq - 8$ by $7$ and simplify.

Divide each term in $7 x \geq - 8$ by $7$ .

$\frac{7 x}{7} \geq \frac{- 8}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} \geq \frac{- 8}{7}$

Divide $x$ by $1$ .

$x \geq \frac{- 8}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x \geq - \frac{8}{7}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{8}{7}$

Interval Notation:

$[- \frac{8}{7}, \infty)$