Finite Math Examples

$\frac{10 k - 3}{9} < 3$

Step 1

Multiply both sides by $9$ .

$\frac{10 k - 3}{9} \cdot 9 < 3 \cdot 9$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $9$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{10 k - 3}{9} \cdot 9 < 3 \cdot 9$

Step 2.1.1.2

Rewrite the expression.

$10 k - 3 < 3 \cdot 9$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $9$ .

$10 k - 3 < 27$

Step 3

Solve for $k$ .

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Step 3.1

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

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Step 3.1.1

Add $3$ to both sides of the inequality.

$10 k < 27 + 3$

Step 3.1.2

Add $27$ and $3$ .

$10 k < 30$

Step 3.2

Divide each term in $10 k < 30$ by $10$ and simplify.

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Step 3.2.1

Divide each term in $10 k < 30$ by $10$ .

$\frac{10 k}{10} < \frac{30}{10}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $10$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{10 k}{10} < \frac{30}{10}$

Step 3.2.2.1.2

Divide $k$ by $1$ .

$k < \frac{30}{10}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $30$ by $10$ .

$k < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$k < 3$

Interval Notation:

$(- \infty, 3)$