Finite Math Examples

$| 8 x - \frac{10}{5} | = 4$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$8 x - \frac{10}{5} = \pm 4$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$8 x - \frac{10}{5} = 4$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Divide $10$ by $5$ .

$8 x - 1 \cdot 2 = 4$

Step 2.2.2

Multiply $- 1$ by $2$ .

$8 x - 2 = 4$

Step 2.3

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.3.1

Add $2$ to both sides of the equation.

$8 x = 4 + 2$

Step 2.3.2

Add $4$ and $2$ .

$8 x = 6$

Step 2.4

Divide each term in $8 x = 6$ by $8$ and simplify.

Tap for more steps...

Step 2.4.1

Divide each term in $8 x = 6$ by $8$ .

$\frac{8 x}{8} = \frac{6}{8}$

Step 2.4.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.4.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{6}{8}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{8}$

Step 2.4.3

Simplify the right side.

Tap for more steps...

Step 2.4.3.1

Cancel the common factor of $6$ and $8$ .

Tap for more steps...

Step 2.4.3.1.1

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{8}$

Step 2.4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.4.3.1.2.1

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 3}{2 \cdot 4}$

Step 2.4.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 4}$

Step 2.4.3.1.2.3

Rewrite the expression.

$x = \frac{3}{4}$

Step 2.5

Next, use the negative value of the $\pm$ to find the second solution.

$8 x - \frac{10}{5} = - 4$

Step 2.6

Simplify each term.

Tap for more steps...

Step 2.6.1

Divide $10$ by $5$ .

$8 x - 1 \cdot 2 = - 4$

Step 2.6.2

Multiply $- 1$ by $2$ .

$8 x - 2 = - 4$

Step 2.7

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.7.1

Add $2$ to both sides of the equation.

$8 x = - 4 + 2$

Step 2.7.2

Add $- 4$ and $2$ .

$8 x = - 2$

Step 2.8

Divide each term in $8 x = - 2$ by $8$ and simplify.

Tap for more steps...

Step 2.8.1

Divide each term in $8 x = - 2$ by $8$ .

$\frac{8 x}{8} = \frac{- 2}{8}$

Step 2.8.2

Simplify the left side.

Tap for more steps...

Step 2.8.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.8.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 2}{8}$

Step 2.8.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{8}$

Step 2.8.3

Simplify the right side.

Tap for more steps...

Step 2.8.3.1

Cancel the common factor of $- 2$ and $8$ .

Tap for more steps...

Step 2.8.3.1.1

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{8}$

Step 2.8.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.8.3.1.2.1

Factor $2$ out of $8$ .

$x = \frac{2 \cdot - 1}{2 \cdot 4}$

Step 2.8.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot - 1}{2 \cdot 4}$

Step 2.8.3.1.2.3

Rewrite the expression.

$x = \frac{- 1}{4}$

Step 2.8.3.2

Move the negative in front of the fraction.

$x = - \frac{1}{4}$

Step 2.9

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{3}{4}, - \frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}, - \frac{1}{4}$

Decimal Form:

$x = 0.75, - 0.25$