Pre-Algebra Examples

$- 6 (z - 5) > 5 z - 3$

Step 1

Simplify $- 6 (z - 5)$ .

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Step 1.1

Rewrite.

$0 + 0 - 6 (z - 5) > 5 z - 3$

Step 1.2

Simplify by adding zeros.

$- 6 (z - 5) > 5 z - 3$

Step 1.3

Apply the distributive property.

$- 6 z - 6 \cdot - 5 > 5 z - 3$

Step 1.4

Multiply $- 6$ by $- 5$ .

$- 6 z + 30 > 5 z - 3$

Step 2

Move all terms containing $z$ to the left side of the inequality.

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Step 2.1

Subtract $5 z$ from both sides of the inequality.

$- 6 z + 30 - 5 z > - 3$

Step 2.2

Subtract $5 z$ from $- 6 z$ .

$- 11 z + 30 > - 3$

Step 3

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

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Step 3.1

Subtract $30$ from both sides of the inequality.

$- 11 z > - 3 - 30$

Step 3.2

Subtract $30$ from $- 3$ .

$- 11 z > - 33$

Step 4

Divide each term in $- 11 z > - 33$ by $- 11$ and simplify.

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Step 4.1

Divide each term in $- 11 z > - 33$ by $- 11$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 11 z}{- 11} < \frac{- 33}{- 11}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 11$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 11 z}{- 11} < \frac{- 33}{- 11}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z < \frac{- 33}{- 11}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 33$ by $- 11$ .

$z < 3$

Step 5