Solve the Inequality for x 2+x<9x+6

$2 + x < 9 x + 6$

Step 1

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

Subtract $9 x$ from both sides of the inequality.

$2 + x - 9 x < 6$

Subtract $9 x$ from $x$ .

$2 - 8 x < 6$

Step 2

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

Subtract $2$ from both sides of the inequality.

$- 8 x < 6 - 2$

Subtract $2$ from $6$ .

$- 8 x < 4$

Step 3

Divide each term in $- 8 x < 4$ by $- 8$ and simplify.

Divide each term in $- 8 x < 4$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} > \frac{4}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} > \frac{4}{- 8}$

Divide $x$ by $1$ .

$x > \frac{4}{- 8}$

Simplify the right side.

Cancel the common factor of $4$ and $- 8$ .

Factor $4$ out of $4$ .

$x > \frac{4 (1)}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$x > \frac{4 \cdot 1}{4 \cdot - 2}$

Cancel the common factor.

$x > \frac{4 \cdot 1}{4 \cdot - 2}$

Rewrite the expression.

$x > \frac{1}{- 2}$

Move the negative in front of the fraction.

$x > - \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{1}{2}$

Interval Notation:

$(- \frac{1}{2}, \infty)$

Solve the Inequality for x 2+x<9x+6

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