Algebra Examples

$5 x + 5 (x - 9) < 10 x - 9$

Step 1

Simplify $5 x + 5 (x - 9)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 x + 5 x + 5 \cdot - 9 < 10 x - 9$

Step 1.1.2

Multiply $5$ by $- 9$ .

$5 x + 5 x - 45 < 10 x - 9$

Step 1.2

Add $5 x$ and $5 x$ .

$10 x - 45 < 10 x - 9$

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.

$10 x - 45 - 10 x < - 9$

Step 2.2

Combine the opposite terms in $10 x - 45 - 10 x$ .

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Step 2.2.1

Subtract $10 x$ from $10 x$ .

$0 - 45 < - 9$

Step 2.2.2

Subtract $45$ from $0$ .

$- 45 < - 9$

Step 3

Since $- 45 < - 9$ , the inequality will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$