Finite Math Examples

$13 x + 4 > 4 (3 x + 1) - x + 5$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$4 (3 x + 1) - x + 5 < 13 x + 4$

Step 2

Simplify $4 (3 x + 1) - x + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 (3 x) + 4 \cdot 1 - x + 5 < 13 x + 4$

Step 2.1.2

Multiply $3$ by $4$ .

$12 x + 4 \cdot 1 - x + 5 < 13 x + 4$

Step 2.1.3

Multiply $4$ by $1$ .

$12 x + 4 - x + 5 < 13 x + 4$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $x$ from $12 x$ .

$11 x + 4 + 5 < 13 x + 4$

Step 2.2.2

Add $4$ and $5$ .

$11 x + 9 < 13 x + 4$

Step 3

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

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Step 3.1

Subtract $13 x$ from both sides of the inequality.

$11 x + 9 - 13 x < 4$

Step 3.2

Subtract $13 x$ from $11 x$ .

$- 2 x + 9 < 4$

Step 4

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

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Step 4.1

Subtract $9$ from both sides of the inequality.

$- 2 x < 4 - 9$

Step 4.2

Subtract $9$ from $4$ .

$- 2 x < - 5$

Step 5

Divide each term in $- 2 x < - 5$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 x < - 5$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

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

Step 6

Convert the inequality to interval notation.

$(\frac{5}{2}, \infty)$

Step 7