Algebra Examples

$84 \geq - 7 (Z - 9)$

Step 1

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

$- 7 (Z - 9) \leq 84$

Step 2

Divide each term in $- 7 (Z - 9) \leq 84$ by $- 7$ and simplify.

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Step 2.1

Divide each term in $- 7 (Z - 9) \leq 84$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 (Z - 9)}{- 7} \geq \frac{84}{- 7}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 7 (Z - 9)}{- 7} \geq \frac{84}{- 7}$

Step 2.2.1.2

Divide $Z - 9$ by $1$ .

$Z - 9 \geq \frac{84}{- 7}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $84$ by $- 7$ .

$Z - 9 \geq - 12$

Step 3

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

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Step 3.1

Add $9$ to both sides of the inequality.

$Z \geq - 12 + 9$

Step 3.2

Add $- 12$ and $9$ .

$Z \geq - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$Z \geq - 3$

Interval Notation:

$[- 3, \infty)$