Algebra Examples

$- 6 > \frac{z}{- 2} + 1$

Step 1

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

$\frac{z}{- 2} + 1 < - 6$

Step 2

Move the negative in front of the fraction.

$- \frac{z}{2} + 1 < - 6$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the inequality.

$- \frac{z}{2} < - 6 - 1$

Step 3.2

Subtract $1$ from $- 6$ .

$- \frac{z}{2} < - 7$

Step 4

Divide each term in $- \frac{z}{2} < - 7$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- \frac{z}{2} < - 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{z}{2}}{- 1} > \frac{- 7}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{z}{2}}{1} > \frac{- 7}{- 1}$

Step 4.2.2

Divide $\frac{z}{2}$ by $1$ .

$\frac{z}{2} > \frac{- 7}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 7$ by $- 1$ .

$\frac{z}{2} > 7$

Step 5

Multiply both sides by $2$ .

$\frac{z}{2} \cdot 2 > 7 \cdot 2$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

$\frac{z}{2} \cdot 2 > 7 \cdot 2$

Step 6.1.1.2

Rewrite the expression.

$z > 7 \cdot 2$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $7$ by $2$ .

$z > 14$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$z > 14$

Interval Notation:

$(14, \infty)$