Algebra Examples

$5 - 3 (6 v + 5) > - 9 v + 10 - 8 v$

Step 1

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

$- 9 v + 10 - 8 v < 5 - 3 (6 v + 5)$

Step 2

Subtract $8 v$ from $- 9 v$ .

$- 17 v + 10 < 5 - 3 (6 v + 5)$

Step 3

Simplify $5 - 3 (6 v + 5)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 17 v + 10 < 5 - 3 (6 v) - 3 \cdot 5$

Step 3.1.2

Multiply $6$ by $- 3$ .

$- 17 v + 10 < 5 - 18 v - 3 \cdot 5$

Step 3.1.3

Multiply $- 3$ by $5$ .

$- 17 v + 10 < 5 - 18 v - 15$

Step 3.2

Subtract $15$ from $5$ .

$- 17 v + 10 < - 18 v - 10$

Step 4

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

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Step 4.1

Add $18 v$ to both sides of the inequality.

$- 17 v + 10 + 18 v < - 10$

Step 4.2

Add $- 17 v$ and $18 v$ .

$v + 10 < - 10$

Step 5

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

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Step 5.1

Subtract $10$ from both sides of the inequality.

$v < - 10 - 10$

Step 5.2

Subtract $10$ from $- 10$ .

$v < - 20$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$v < - 20$

Interval Notation:

$(- \infty, - 20)$