Finite Math Examples

$- 2 (4 x - 14) < 10 x + 12$

Step 1

Simplify $- 2 (4 x - 14)$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (4 x - 14) < 10 x + 12$

Step 1.2

Simplify by adding zeros.

$- 2 (4 x - 14) < 10 x + 12$

Step 1.3

Apply the distributive property.

$- 2 (4 x) - 2 \cdot - 14 < 10 x + 12$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $4$ by $- 2$ .

$- 8 x - 2 \cdot - 14 < 10 x + 12$

Step 1.4.2

Multiply $- 2$ by $- 14$ .

$- 8 x + 28 < 10 x + 12$

Step 2

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

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Step 2.1

Subtract $10 x$ from both sides of the inequality.

$- 8 x + 28 - 10 x < 12$

Step 2.2

Subtract $10 x$ from $- 8 x$ .

$- 18 x + 28 < 12$

Step 3

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

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Step 3.1

Subtract $28$ from both sides of the inequality.

$- 18 x < 12 - 28$

Step 3.2

Subtract $28$ from $12$ .

$- 18 x < - 16$

Step 4

Divide each term in $- 18 x < - 16$ by $- 18$ and simplify.

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Step 4.1

Divide each term in $- 18 x < - 16$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 x}{- 18} > \frac{- 16}{- 18}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 18$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 18 x}{- 18} > \frac{- 16}{- 18}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 16}{- 18}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 16$ and $- 18$ .

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Step 4.3.1.1

Factor $- 2$ out of $- 16$ .

$x > \frac{- 2 (8)}{- 18}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $- 2$ out of $- 18$ .

$x > \frac{- 2 \cdot 8}{- 2 \cdot 9}$

Step 4.3.1.2.2

Cancel the common factor.

$x > \frac{- 2 \cdot 8}{- 2 \cdot 9}$

Step 4.3.1.2.3

Rewrite the expression.

$x > \frac{8}{9}$

Step 5

Convert the inequality to interval notation.

$(\frac{8}{9}, \infty)$

Step 6