Finite Math Examples

$\frac{1}{2} x - 5 > 12$

Step 1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - 5 > 12$

Step 2

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

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Step 2.1

Add $5$ to both sides of the inequality.

$\frac{x}{2} > 12 + 5$

Step 2.2

Add $12$ and $5$ .

$\frac{x}{2} > 17$

Step 3

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 > 17 \cdot 2$

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 $2$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{x}{2} \cdot 2 > 17 \cdot 2$

Step 4.1.1.2

Rewrite the expression.

$x > 17 \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $17$ by $2$ .

$x > 34$

Step 5

Convert the inequality to interval notation.

$(34, \infty)$

Step 6