Solve the System of Inequalities -2x-7>1 or x-2>=-1

$- 2 x - 7 > 1$ or $x - 2 \geq - 1$

Step 1

Simplify the first inequality.

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

Add $7$ to both sides of the inequality.

$- 2 x > 1 + 7$ or $x - 2 \geq - 1$

Add $1$ and $7$ .

$- 2 x > 8$ or $x - 2 \geq - 1$

Divide each term in $- 2 x > 8$ by $- 2$ and simplify.

Divide each term in $- 2 x > 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{8}{- 2}$ or $x - 2 \geq - 1$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{8}{- 2}$ or $x - 2 \geq - 1$

Divide $x$ by $1$ .

$x < \frac{8}{- 2}$ or $x - 2 \geq - 1$

Simplify the right side.

Divide $8$ by $- 2$ .

$x < - 4$ or $x - 2 \geq - 1$

Step 2

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

Add $2$ to both sides of the inequality.

$x < - 4$ or $x \geq - 1 + 2$

Add $- 1$ and $2$ .

$x < - 4$ or $x \geq 1$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 4 or x \geq 1$

Interval Notation:

$(- \infty, - 4) \cup [1, \infty)$

Step 4

Solve the System of Inequalities -2x-7>1 or x-2>=-1

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