Finite Math Examples

$9 x - 1 < 34 (20 x - 6)$

Step 1

Simplify $34 (20 x - 6)$ .

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Step 1.1

Rewrite.

$9 x - 1 < 0 + 0 + 34 (20 x - 6)$

Step 1.2

Simplify by adding zeros.

$9 x - 1 < 34 (20 x - 6)$

Step 1.3

Apply the distributive property.

$9 x - 1 < 34 (20 x) + 34 \cdot - 6$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $20$ by $34$ .

$9 x - 1 < 680 x + 34 \cdot - 6$

Step 1.4.2

Multiply $34$ by $- 6$ .

$9 x - 1 < 680 x - 204$

Step 2

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

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Step 2.1

Subtract $680 x$ from both sides of the inequality.

$9 x - 1 - 680 x < - 204$

Step 2.2

Subtract $680 x$ from $9 x$ .

$- 671 x - 1 < - 204$

Step 3

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

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Step 3.1

Add $1$ to both sides of the inequality.

$- 671 x < - 204 + 1$

Step 3.2

Add $- 204$ and $1$ .

$- 671 x < - 203$

Step 4

Divide each term in $- 671 x < - 203$ by $- 671$ and simplify.

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Step 4.1

Divide each term in $- 671 x < - 203$ by $- 671$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 671 x}{- 671} > \frac{- 203}{- 671}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 671$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 671 x}{- 671} > \frac{- 203}{- 671}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 203}{- 671}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$x > \frac{203}{671}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{203}{671}$

Interval Notation:

$(\frac{203}{671}, \infty)$