Algebra Examples

$5 - (x + 5) > - 2 (x + 4)$

Step 1

Simplify $5 - (x + 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 - x - 1 \cdot 5 > - 2 (x + 4)$

Step 1.1.2

Multiply $- 1$ by $5$ .

$5 - x - 5 > - 2 (x + 4)$

$5 - x - 5 > - 2 (x + 4)$

Step 1.2

Combine the opposite terms in $5 - x - 5$ .

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Step 1.2.1

Subtract $5$ from $5$ .

$- x + 0 > - 2 (x + 4)$

Step 1.2.2

Add $- x$ and $0$ .

$- x > - 2 (x + 4)$

$- x > - 2 (x + 4)$

$- x > - 2 (x + 4)$

Step 2

Simplify $- 2 (x + 4)$ .

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Step 2.1

Apply the distributive property.

$- x > - 2 x - 2 \cdot 4$

Step 2.2

Multiply $- 2$ by $4$ .

$- x > - 2 x - 8$

$- x > - 2 x - 8$

Step 3

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

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Step 3.1

Add $2 x$ to both sides of the inequality.

$- x + 2 x > - 8$

Step 3.2

Add $- x$ and $2 x$ .

$x > - 8$

$x > - 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - 8$

Interval Notation:

$(- 8, \infty)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$