Finite Math Examples

$0.05 x + 21.45 < 2 (2.2 x - 1.5) + 3.8 x$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$2 (2.2 x - 1.5) + 3.8 x > 0.05 x + 21.45$

Step 2

Simplify $2 (2.2 x - 1.5) + 3.8 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 (2.2 x) + 2 \cdot - 1.5 + 3.8 x > 0.05 x + 21.45$

Step 2.1.2

Multiply $2.2$ by $2$ .

$4.4 x + 2 \cdot - 1.5 + 3.8 x > 0.05 x + 21.45$

Step 2.1.3

Multiply $2$ by $- 1.5$ .

$4.4 x - 3 + 3.8 x > 0.05 x + 21.45$

Step 2.2

Add $4.4 x$ and $3.8 x$ .

$8.2 x - 3 > 0.05 x + 21.45$

Step 3

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

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Step 3.1

Subtract $0.05 x$ from both sides of the inequality.

$8.2 x - 3 - 0.05 x > 21.45$

Step 3.2

Subtract $0.05 x$ from $8.2 x$ .

$8.15 x - 3 > 21.45$

Step 4

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

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Step 4.1

Add $3$ to both sides of the inequality.

$8.15 x > 21.45 + 3$

Step 4.2

Add $21.45$ and $3$ .

$8.15 x > 24.45$

Step 5

Divide each term in $8.15 x > 24.45$ by $8.15$ and simplify.

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Step 5.1

Divide each term in $8.15 x > 24.45$ by $8.15$ .

$\frac{8.15 x}{8.15} > \frac{24.45}{8.15}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $8.15$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{8.15 x}{8.15} > \frac{24.45}{8.15}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{24.45}{8.15}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $24.45$ by $8.15$ .

$x > 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 3$

Interval Notation:

$(3, \infty)$