Finite Math Examples

$- 2 (2 x + 7) < 2 (- 5 x + 5)$

Step 1

Simplify $- 2 (2 x + 7)$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (2 x + 7) < 2 (- 5 x + 5)$

Step 1.2

Simplify by adding zeros.

$- 2 (2 x + 7) < 2 (- 5 x + 5)$

Step 1.3

Apply the distributive property.

$- 2 (2 x) - 2 \cdot 7 < 2 (- 5 x + 5)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $- 2$ .

$- 4 x - 2 \cdot 7 < 2 (- 5 x + 5)$

Step 1.4.2

Multiply $- 2$ by $7$ .

$- 4 x - 14 < 2 (- 5 x + 5)$

Step 2

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

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Step 2.1

Apply the distributive property.

$- 4 x - 14 < 2 (- 5 x) + 2 \cdot 5$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $- 5$ by $2$ .

$- 4 x - 14 < - 10 x + 2 \cdot 5$

Step 2.2.2

Multiply $2$ by $5$ .

$- 4 x - 14 < - 10 x + 10$

Step 3

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

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Step 3.1

Add $10 x$ to both sides of the inequality.

$- 4 x - 14 + 10 x < 10$

Step 3.2

Add $- 4 x$ and $10 x$ .

$6 x - 14 < 10$

Step 4

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

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Step 4.1

Add $14$ to both sides of the inequality.

$6 x < 10 + 14$

Step 4.2

Add $10$ and $14$ .

$6 x < 24$

Step 5

Divide each term in $6 x < 24$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 x < 24$ by $6$ .

$\frac{6 x}{6} < \frac{24}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 x}{6} < \frac{24}{6}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{24}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $24$ by $6$ .

$x < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 4$

Interval Notation:

$(- \infty, 4)$