Finite Math Examples

$2 < \frac{x - 4}{2} < 17$

Step 1

Multiply each term in the inequality by $2$ .

$2 \cdot 2 < \frac{x - 4}{2} \cdot 2 < 17 \cdot 2$

Step 2

Multiply $2$ by $2$ .

$4 < \frac{x - 4}{2} \cdot 2 < 17 \cdot 2$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$4 < \frac{x - 4}{2} \cdot 2 < 17 \cdot 2$

Step 3.2

Rewrite the expression.

$4 < x - 4 < 17 \cdot 2$

Step 4

Multiply $17$ by $2$ .

$4 < x - 4 < 34$

Step 5

Move all terms not containing $x$ from the center section of the inequality.

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Step 5.1

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$4 + 4 < x < 34 + 4$

Step 5.2

Add $4$ and $4$ .

$8 < x < 34 + 4$

Step 5.3

Add $34$ and $4$ .

$8 < x < 38$

Step 6

Convert the inequality to interval notation.

$(8, 38)$

Step 7