Finite Math Examples

$\frac{x - 7}{2} < 2$

Step 1

Multiply both sides by $2$ .

$\frac{x - 7}{2} \cdot 2 < 2 \cdot 2$

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 $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x - 7}{2} \cdot 2 < 2 \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$x - 7 < 2 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $2$ .

$x - 7 < 4$

Step 3

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

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Step 3.1

Add $7$ to both sides of the inequality.

$x < 4 + 7$

Step 3.2

Add $4$ and $7$ .

$x < 11$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 11$

Interval Notation:

$(- \infty, 11)$