Algebra Examples

$2 (a - 8) \geq - 2 a$

Step 1

Simplify $2 (a - 8)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (a - 8) \geq - 2 a$

Step 1.2

Simplify by adding zeros.

$2 (a - 8) \geq - 2 a$

Step 1.3

Apply the distributive property.

$2 a + 2 \cdot - 8 \geq - 2 a$

Step 1.4

Multiply $2$ by $- 8$ .

$2 a - 16 \geq - 2 a$

Step 2

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

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Step 2.1

Add $2 a$ to both sides of the inequality.

$2 a - 16 + 2 a \geq 0$

Step 2.2

Add $2 a$ and $2 a$ .

$4 a - 16 \geq 0$

Step 3

Add $16$ to both sides of the inequality.

$4 a \geq 16$

Step 4

Divide each term in $4 a \geq 16$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 a \geq 16$ by $4$ .

$\frac{4 a}{4} \geq \frac{16}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 a}{4} \geq \frac{16}{4}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a \geq \frac{16}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $16$ by $4$ .

$a \geq 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$a \geq 4$

Interval Notation:

$[4, \infty)$