Algebra Examples

$55 > - 7 v + 6$

Step 1

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

$- 7 v + 6 < 55$

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the inequality.

$- 7 v < 55 - 6$

Step 2.2

Subtract $6$ from $55$ .

$- 7 v < 49$

Step 3

Divide each term in $- 7 v < 49$ by $- 7$ and simplify.

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Step 3.1

Divide each term in $- 7 v < 49$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 v}{- 7} > \frac{49}{- 7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 7 v}{- 7} > \frac{49}{- 7}$

Step 3.2.1.2

Divide $v$ by $1$ .

$v > \frac{49}{- 7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $49$ by $- 7$ .

$v > - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$v > - 7$

Interval Notation:

$(- 7, \infty)$