Finite Math Examples

∣ ∣ ∣ 7 \frac{1}{3} ∣ ∣ ∣

$| 7 \frac{1}{3} |$

Step 1

Set

∣ ∣ ∣ 7 \frac{1}{3} ∣ ∣ ∣

$| 7 \frac{1}{3} |$ equal to

0

$0$ .

∣ ∣ ∣ 7 \frac{1}{3} ∣ ∣ ∣ = 0

$| 7 \frac{1}{3} | = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify

∣ ∣ ∣ 7 \frac{1}{3} ∣ ∣ ∣

$| 7 \frac{1}{3} |$ .

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Step 2.1.1.1

Convert

7 \frac{1}{3}

$7 \frac{1}{3}$ to an improper fraction.

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Step 2.1.1.1.1

A mixed number is an addition of its whole and fractional parts.

∣ ∣ ∣ 7 + \frac{1}{3} ∣ ∣ ∣ = 0

$| 7 + \frac{1}{3} | = 0$

Step 2.1.1.1.2

Add

7

$7$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 2.1.1.1.2.1

To write

7

$7$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

∣ ∣ ∣ 7 \cdot \frac{3}{3} + \frac{1}{3} ∣ ∣ ∣ = 0

$| 7 \cdot \frac{3}{3} + \frac{1}{3} | = 0$

Step 2.1.1.1.2.2

Combine

7

$7$ and

\frac{3}{3}

$\frac{3}{3}$ .

∣ ∣ ∣ \frac{7 \cdot 3}{3} + \frac{1}{3} ∣ ∣ ∣ = 0

$| \frac{7 \cdot 3}{3} + \frac{1}{3} | = 0$

Step 2.1.1.1.2.3

Combine the numerators over the common denominator.

∣ ∣ ∣ \frac{7 \cdot 3 + 1}{3} ∣ ∣ ∣ = 0

$| \frac{7 \cdot 3 + 1}{3} | = 0$

Step 2.1.1.1.2.4

Simplify the numerator.

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Step 2.1.1.1.2.4.1

Multiply

7

$7$ by

3

$3$ .

∣ ∣ ∣ \frac{21 + 1}{3} ∣ ∣ ∣ = 0

$| \frac{21 + 1}{3} | = 0$

Step 2.1.1.1.2.4.2

Add

$21$ and

$1$ .

$| \frac{22}{3} | = 0$

Step 2.1.1.2

$\frac{22}{3}$ is approximately

$7.\overline{3}$ which is positive so remove the absolute value

$\frac{22}{3} = 0$

Step 2.2

Set the numerator equal to zero.

$22 = 0$

Step 2.3

Since

$22 \neq 0$ , there are no solutions.

No solution