Algebra Examples

$\frac{1}{2} h + 2 \geq \frac{1}{2} (h + 8)$

Step 1

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

$\frac{h}{2} + 2 \geq \frac{1}{2} \cdot (h + 8)$

Step 2

Simplify $\frac{1}{2} \cdot (h + 8)$ .

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Step 2.1

Apply the distributive property.

$\frac{h}{2} + 2 \geq \frac{1}{2} h + \frac{1}{2} \cdot 8$

Step 2.2

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

$\frac{h}{2} + 2 \geq \frac{h}{2} + \frac{1}{2} \cdot 8$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $8$ .

$\frac{h}{2} + 2 \geq \frac{h}{2} + \frac{1}{2} \cdot (2 (4))$

Step 2.3.2

Cancel the common factor.

$\frac{h}{2} + 2 \geq \frac{h}{2} + \frac{1}{2} \cdot (2 \cdot 4)$

Step 2.3.3

Rewrite the expression.

$\frac{h}{2} + 2 \geq \frac{h}{2} + 4$

Step 3

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

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Step 3.1

Subtract $\frac{h}{2}$ from both sides of the inequality.

$\frac{h}{2} + 2 - \frac{h}{2} \geq 4$

Step 3.2

Combine the opposite terms in $\frac{h}{2} + 2 - \frac{h}{2}$ .

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Step 3.2.1

Subtract $\frac{h}{2}$ from $\frac{h}{2}$ .

$0 + 2 \geq 4$

Step 3.2.2

Add $0$ and $2$ .

$2 \geq 4$

Step 4

Since $2 \neq 4$ , there are no solutions.

No solution