Finite Math Examples

$\frac{11}{10} \cdot (x + 30) < 50$

Step 1

Simplify $\frac{11}{10} \cdot (x + 30)$ .

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Step 1.1

Apply the distributive property.

$\frac{11}{10} x + \frac{11}{10} \cdot 30 < 50$

Step 1.2

Combine $\frac{11}{10}$ and $x$ .

$\frac{11 x}{10} + \frac{11}{10} \cdot 30 < 50$

Step 1.3

Cancel the common factor of $10$ .

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Step 1.3.1

Factor $10$ out of $30$ .

$\frac{11 x}{10} + \frac{11}{10} \cdot (10 (3)) < 50$

Step 1.3.2

Cancel the common factor.

$\frac{11 x}{10} + \frac{11}{10} \cdot (10 \cdot 3) < 50$

Step 1.3.3

Rewrite the expression.

$\frac{11 x}{10} + 11 \cdot 3 < 50$

Step 1.4

Multiply $11$ by $3$ .

$\frac{11 x}{10} + 33 < 50$

Step 2

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

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Step 2.1

Subtract $33$ from both sides of the inequality.

$\frac{11 x}{10} < 50 - 33$

Step 2.2

Subtract $33$ from $50$ .

$\frac{11 x}{10} < 17$

Step 3

Multiply both sides by $10$ .

$\frac{11 x}{10} \cdot 10 < 17 \cdot 10$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{11 x}{10} \cdot 10 < 17 \cdot 10$

Step 4.1.1.2

Rewrite the expression.

$11 x < 17 \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $17$ by $10$ .

$11 x < 170$

Step 5

Divide each term in $11 x < 170$ by $11$ and simplify.

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Step 5.1

Divide each term in $11 x < 170$ by $11$ .

$\frac{11 x}{11} < \frac{170}{11}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $11$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{11 x}{11} < \frac{170}{11}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{170}{11}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{170}{11}$

Interval Notation:

$(- \infty, \frac{170}{11})$