Finite Math Examples

$2 v - 2 < 4$ , $4 v + 3 > 27$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Add $2$ to both sides of the inequality.

$2 v < 4 + 2$ and $4 v + 3 > 27$

Step 1.1.2

Add $4$ and $2$ .

$2 v < 6$ and $4 v + 3 > 27$

Step 1.2

Divide each term in $2 v < 6$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 v < 6$ by $2$ .

$\frac{2 v}{2} < \frac{6}{2}$ and $4 v + 3 > 27$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 v}{2} < \frac{6}{2}$ and $4 v + 3 > 27$

Step 1.2.2.1.2

Divide $v$ by $1$ .

$v < \frac{6}{2}$ and $4 v + 3 > 27$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $6$ by $2$ .

$v < 3$ and $4 v + 3 > 27$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Subtract $3$ from both sides of the inequality.

$v < 3$ and $4 v > 27 - 3$

Step 2.1.2

Subtract $3$ from $27$ .

$v < 3$ and $4 v > 24$

Step 2.2

Divide each term in $4 v > 24$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 v > 24$ by $4$ .

$v < 3$ and $\frac{4 v}{4} > \frac{24}{4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$v < 3$ and $\frac{4 v}{4} > \frac{24}{4}$

Step 2.2.2.1.2

Divide $v$ by $1$ .

$v < 3$ and $v > \frac{24}{4}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $24$ by $4$ .

$v < 3$ and $v > 6$

Step 3

The intersection consists of the elements that are contained in both intervals.

No solution