Finite Math Examples

$10 (\frac{1}{2} x + 4) < 10 (\frac{1}{2} x - 3)$

Step 1

Simplify $10 (\frac{1}{2} x + 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + 10 (\frac{1}{2} x + 4) < 10 (\frac{1}{2} x - 3)$

Step 1.2

Simplify by adding zeros.

$10 (\frac{1}{2} x + 4) < 10 (\frac{1}{2} x - 3)$

Step 1.3

Combine $\frac{1}{2}$ and $x$ .

$10 (\frac{x}{2} + 4) < 10 (\frac{1}{2} x - 3)$

Step 1.4

Apply the distributive property.

$10 \frac{x}{2} + 10 \cdot 4 < 10 (\frac{1}{2} x - 3)$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $10$ .

$2 (5) \frac{x}{2} + 10 \cdot 4 < 10 (\frac{1}{2} x - 3)$

Step 1.5.2

Cancel the common factor.

$2 \cdot 5 \frac{x}{2} + 10 \cdot 4 < 10 (\frac{1}{2} x - 3)$

Step 1.5.3

Rewrite the expression.

$5 x + 10 \cdot 4 < 10 (\frac{1}{2} x - 3)$

Step 1.6

Multiply $10$ by $4$ .

$5 x + 40 < 10 (\frac{1}{2} x - 3)$

Step 2

Simplify $10 (\frac{1}{2} x - 3)$ .

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Step 2.1

Combine $\frac{1}{2}$ and $x$ .

$5 x + 40 < 10 (\frac{x}{2} - 3)$

Step 2.2

Apply the distributive property.

$5 x + 40 < 10 \frac{x}{2} + 10 \cdot - 3$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $10$ .

$5 x + 40 < 2 (5) \frac{x}{2} + 10 \cdot - 3$

Step 2.3.2

Cancel the common factor.

$5 x + 40 < 2 \cdot 5 \frac{x}{2} + 10 \cdot - 3$

Step 2.3.3

Rewrite the expression.

$5 x + 40 < 5 x + 10 \cdot - 3$

Step 2.4

Multiply $10$ by $- 3$ .

$5 x + 40 < 5 x - 30$

Step 3

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

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Step 3.1

Subtract $5 x$ from both sides of the inequality.

$5 x + 40 - 5 x < - 30$

Step 3.2

Combine the opposite terms in $5 x + 40 - 5 x$ .

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Step 3.2.1

Subtract $5 x$ from $5 x$ .

$0 + 40 < - 30$

Step 3.2.2

Add $0$ and $40$ .

$40 < - 30$

Step 4

Since $40 > - 30$ , there are no solutions.

No solution