Calculus Examples

$- 5 (z - 2) > 3 z - 6$

Step 1

Simplify $- 5 (z - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 - 5 (z - 2) > 3 z - 6$

Step 1.2

Simplify by adding zeros.

$- 5 (z - 2) > 3 z - 6$

Step 1.3

Apply the distributive property.

$- 5 z - 5 \cdot - 2 > 3 z - 6$

Step 1.4

Multiply $- 5$ by $- 2$ .

$- 5 z + 10 > 3 z - 6$

Step 2

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

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Step 2.1

Subtract $3 z$ from both sides of the inequality.

$- 5 z + 10 - 3 z > - 6$

Step 2.2

Subtract $3 z$ from $- 5 z$ .

$- 8 z + 10 > - 6$

Step 3

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

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Step 3.1

Subtract $10$ from both sides of the inequality.

$- 8 z > - 6 - 10$

Step 3.2

Subtract $10$ from $- 6$ .

$- 8 z > - 16$

Step 4

Divide each term in $- 8 z > - 16$ by $- 8$ and simplify.

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Step 4.1

Divide each term in $- 8 z > - 16$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 z}{- 8} < \frac{- 16}{- 8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 8 z}{- 8} < \frac{- 16}{- 8}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z < \frac{- 16}{- 8}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 16$ by $- 8$ .

$z < 2$

Step 5

Convert the inequality to interval notation.

$(- \infty, 2)$

Step 6