Algebra Examples

$\frac{10 | - 2 |}{4} + | - 2 - 5 |$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $10$ and $4$ .

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Step 1.1.1

Factor $2$ out of $10 | - 2 |$ .

$\frac{2 (5 | - 2 |)}{4} + | - 2 - 5 |$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $4$ .

$\frac{2 (5 | - 2 |)}{2 (2)} + | - 2 - 5 |$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 (5 | - 2 |)}{2 \cdot 2} + | - 2 - 5 |$

Step 1.1.2.3

Rewrite the expression.

$\frac{5 | - 2 |}{2} + | - 2 - 5 |$

Step 1.2

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$\frac{5 \cdot 2}{2} + | - 2 - 5 |$

Step 1.3

Multiply $5$ by $2$ .

$\frac{10}{2} + | - 2 - 5 |$

Step 1.4

Divide $10$ by $2$ .

$5 + | - 2 - 5 |$

Step 1.5

Subtract $5$ from $- 2$ .

$5 + | - 7 |$

Step 1.6

The absolute value is the distance between a number and zero. The distance between $- 7$ and $0$ is $7$ .

$5 + 7$

Step 2

Add $5$ and $7$ .

$12$