Finite Math Examples

$2 (2 - 8 x) + 5 x < 6 (3 + 5 x)$

Step 1

Simplify $2 (2 - 8 x) + 5 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 \cdot 2 + 2 (- 8 x) + 5 x < 6 (3 + 5 x)$

Step 1.1.2

Multiply $2$ by $2$ .

$4 + 2 (- 8 x) + 5 x < 6 (3 + 5 x)$

Step 1.1.3

Multiply $- 8$ by $2$ .

$4 - 16 x + 5 x < 6 (3 + 5 x)$

Step 1.2

Add $- 16 x$ and $5 x$ .

$4 - 11 x < 6 (3 + 5 x)$

Step 2

Simplify $6 (3 + 5 x)$ .

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Step 2.1

Apply the distributive property.

$4 - 11 x < 6 \cdot 3 + 6 (5 x)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $6$ by $3$ .

$4 - 11 x < 18 + 6 (5 x)$

Step 2.2.2

Multiply $5$ by $6$ .

$4 - 11 x < 18 + 30 x$

Step 3

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

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Step 3.1

Subtract $30 x$ from both sides of the inequality.

$4 - 11 x - 30 x < 18$

Step 3.2

Subtract $30 x$ from $- 11 x$ .

$4 - 41 x < 18$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the inequality.

$- 41 x < 18 - 4$

Step 4.2

Subtract $4$ from $18$ .

$- 41 x < 14$

Step 5

Divide each term in $- 41 x < 14$ by $- 41$ and simplify.

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Step 5.1

Divide each term in $- 41 x < 14$ by $- 41$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 41 x}{- 41} > \frac{14}{- 41}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 41$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 41 x}{- 41} > \frac{14}{- 41}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{14}{- 41}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x > - \frac{14}{41}$

Step 6

Convert the inequality to interval notation.

$(- \frac{14}{41}, \infty)$

Step 7