Solve the Inequality for x -x-1>3x+1

$- x - 1 > 3 x + 1$

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

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

$- x - 1 - 3 x > 1$

Subtract $3 x$ from $- x$ .

$- 4 x - 1 > 1$

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

Add $1$ to both sides of the inequality.

$- 4 x > 1 + 1$

Add $1$ and $1$ .

$- 4 x > 2$

Divide each term in $- 4 x > 2$ by $- 4$ and simplify.

Divide each term in $- 4 x > 2$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{2}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{2}{- 4}$

Divide $x$ by $1$ .

$x < \frac{2}{- 4}$

Simplify the right side.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$x < \frac{2 (1)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$x < \frac{2 \cdot 1}{2 \cdot - 2}$

Cancel the common factor.

$x < \frac{2 \cdot 1}{2 \cdot - 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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

Solve the Inequality for x -x-1>3x+1

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