Finite Math Examples

$x + 0.035 \cdot (5 - 1.055 \cdot 3.8) > (0.15825 + 0.035 \cdot 5) + 0.6 \cdot (0.81475 - 0.035 \cdot 5) \cdot x$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 1.055$ by $3.8$ .

$x + 0.035 \cdot (5 - 4.009) > 0.15825 + 0.035 \cdot 5 + 0.6 \cdot (0.81475 - 0.035 \cdot 5) \cdot x$

Step 1.2

Subtract $4.009$ from $5$ .

$x + 0.035 \cdot 0.991 > 0.15825 + 0.035 \cdot 5 + 0.6 \cdot (0.81475 - 0.035 \cdot 5) \cdot x$

Step 1.3

Multiply $0.035$ by $0.991$ .

$x + 0.034685 > 0.15825 + 0.035 \cdot 5 + 0.6 \cdot (0.81475 - 0.035 \cdot 5) \cdot x$

Step 2

Simplify $0.15825 + 0.035 \cdot 5 + 0.6 \cdot (0.81475 - 0.035 \cdot 5) \cdot x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $0.035$ by $5$ .

$x + 0.034685 > 0.15825 + 0.175 + 0.6 \cdot (0.81475 - 0.035 \cdot 5) \cdot x$

Step 2.1.2

Multiply $- 0.035$ by $5$ .

$x + 0.034685 > 0.15825 + 0.175 + 0.6 \cdot (0.81475 - 0.175) \cdot x$

Step 2.1.3

Subtract $0.175$ from $0.81475$ .

$x + 0.034685 > 0.15825 + 0.175 + 0.6 \cdot 0.63975 \cdot x$

Step 2.1.4

Multiply $0.6$ by $0.63975$ .

$x + 0.034685 > 0.15825 + 0.175 + 0.38385 x$

Step 2.2

Add $0.15825$ and $0.175$ .

$x + 0.034685 > 0.33325 + 0.38385 x$

Step 3

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

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Step 3.1

Subtract $0.38385 x$ from both sides of the inequality.

$x + 0.034685 - 0.38385 x > 0.33325$

Step 3.2

Subtract $0.38385 x$ from $x$ .

$0.61615 x + 0.034685 > 0.33325$

Step 4

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

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Step 4.1

Subtract $0.034685$ from both sides of the inequality.

$0.61615 x > 0.33325 - 0.034685$

Step 4.2

Subtract $0.034685$ from $0.33325$ .

$0.61615 x > 0.298565$

Step 5

Divide each term in $0.61615 x > 0.298565$ by $0.61615$ and simplify.

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Step 5.1

Divide each term in $0.61615 x > 0.298565$ by $0.61615$ .

$\frac{0.61615 x}{0.61615} > \frac{0.298565}{0.61615}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $0.61615$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{0.61615 x}{0.61615} > \frac{0.298565}{0.61615}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{0.298565}{0.61615}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0.298565$ by $0.61615$ .

$x > 0.48456544$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 0.48456544$

Interval Notation:

$(0.48456544, \infty)$