Finite Math Examples

$7 x - 2 > 5 x + 8$

Step 1

Move all terms containing $x$ to the left side of the inequality.

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Step 1.1

Subtract $5 x$ from both sides of the inequality.

$7 x - 2 - 5 x > 8$

Step 1.2

Subtract $5 x$ from $7 x$ .

$2 x - 2 > 8$

Step 2

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

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Step 2.1

Add $2$ to both sides of the inequality.

$2 x > 8 + 2$

Step 2.2

Add $8$ and $2$ .

$2 x > 10$

Step 3

Divide each term in $2 x > 10$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x > 10$ by $2$ .

$\frac{2 x}{2} > \frac{10}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} > \frac{10}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{10}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $10$ by $2$ .

$x > 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 5$

Interval Notation:

$(5, \infty)$