Algebra Examples

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

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Add $7$ to both sides of the inequality.

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

Step 1.1.2

Add $1$ and $7$ .

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

Step 1.2

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

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Step 1.2.1

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 $x - 2 \geq - 1$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

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.

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Step 2.1

Add $2$ to both sides of the inequality.

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

Step 2.2

Add $- 1$ and $2$ .

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

Step 3

Convert the inequality to interval notation.

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

Step 4