Pre-Algebra Examples

$- 53 > - 3 (3 z + 3) + 3 z$

Step 1

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

$- 3 (3 z + 3) + 3 z < - 53$

Step 2

Simplify $- 3 (3 z + 3) + 3 z$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 3 (3 z) - 3 \cdot 3 + 3 z < - 53$

Step 2.1.2

Multiply $3$ by $- 3$ .

$- 9 z - 3 \cdot 3 + 3 z < - 53$

Step 2.1.3

Multiply $- 3$ by $3$ .

$- 9 z - 9 + 3 z < - 53$

Step 2.2

Add $- 9 z$ and $3 z$ .

$- 6 z - 9 < - 53$

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.

$- 6 z < - 53 + 9$

Step 3.2

Add $- 53$ and $9$ .

$- 6 z < - 44$

Step 4

Divide each term in $- 6 z < - 44$ by $- 6$ and simplify.

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Step 4.1

Divide each term in $- 6 z < - 44$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 z}{- 6} > \frac{- 44}{- 6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 6 z}{- 6} > \frac{- 44}{- 6}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z > \frac{- 44}{- 6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 44$ and $- 6$ .

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Step 4.3.1.1

Factor $- 2$ out of $- 44$ .

$z > \frac{- 2 (22)}{- 6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $- 2$ out of $- 6$ .

$z > \frac{- 2 \cdot 22}{- 2 \cdot 3}$

Step 4.3.1.2.2

Cancel the common factor.

$z > \frac{- 2 \cdot 22}{- 2 \cdot 3}$

Step 4.3.1.2.3

Rewrite the expression.

$z > \frac{22}{3}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$z > \frac{22}{3}$

Interval Notation:

$(\frac{22}{3}, \infty)$