Finite Math Examples

$| 8 x - 10 | = | 8 + 4 x |$

Step 1

Rewrite the equation as $| 8 + 4 x | = | 8 x - 10 |$ .

$| 8 + 4 x | = | 8 x - 10 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$8 + 4 x = 8 x - 10$

$8 + 4 x = - (8 x - 10)$

$- (8 + 4 x) = 8 x - 10$

$- (8 + 4 x) = - (8 x - 10)$

Step 3

After simplifying, there are only two unique equations to be solved.

$8 + 4 x = 8 x - 10$

$8 + 4 x = - (8 x - 10)$

Step 4

Solve $8 + 4 x = 8 x - 10$ for $x$ .

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Subtract $8 x$ from both sides of the equation.

$8 + 4 x - 8 x = - 10$

Step 4.1.2

Subtract $8 x$ from $4 x$ .

$8 - 4 x = - 10$

Step 4.2

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

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Step 4.2.1

Subtract $8$ from both sides of the equation.

$- 4 x = - 10 - 8$

Step 4.2.2

Subtract $8$ from $- 10$ .

$- 4 x = - 18$

Step 4.3

Divide each term in $- 4 x = - 18$ by $- 4$ and simplify.

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Step 4.3.1

Divide each term in $- 4 x = - 18$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 18}{- 4}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 4$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 18}{- 4}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 18}{- 4}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $- 18$ and $- 4$ .

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Step 4.3.3.1.1

Factor $- 2$ out of $- 18$ .

$x = \frac{- 2 (9)}{- 4}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $- 2$ out of $- 4$ .

$x = \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Step 4.3.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Step 4.3.3.1.2.3

Rewrite the expression.

$x = \frac{9}{2}$

Step 5

Solve $8 + 4 x = - (8 x - 10)$ for $x$ .

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Step 5.1

Simplify $- (8 x - 10)$ .

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Step 5.1.1

Rewrite.

$8 + 4 x = 0 + 0 - (8 x - 10)$

Step 5.1.2

Simplify by adding zeros.

$8 + 4 x = - (8 x - 10)$

Step 5.1.3

Apply the distributive property.

$8 + 4 x = - (8 x) - - 10$

Step 5.1.4

Multiply.

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Step 5.1.4.1

Multiply $8$ by $- 1$ .

$8 + 4 x = - 8 x - - 10$

Step 5.1.4.2

Multiply $- 1$ by $- 10$ .

$8 + 4 x = - 8 x + 10$

Step 5.2

Move all terms containing $x$ to the left side of the equation.

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Step 5.2.1

Add $8 x$ to both sides of the equation.

$8 + 4 x + 8 x = 10$

Step 5.2.2

Add $4 x$ and $8 x$ .

$8 + 12 x = 10$

Step 5.3

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

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Step 5.3.1

Subtract $8$ from both sides of the equation.

$12 x = 10 - 8$

Step 5.3.2

Subtract $8$ from $10$ .

$12 x = 2$

Step 5.4

Divide each term in $12 x = 2$ by $12$ and simplify.

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Step 5.4.1

Divide each term in $12 x = 2$ by $12$ .

$\frac{12 x}{12} = \frac{2}{12}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $12$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{2}{12}$

Step 5.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{12}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Cancel the common factor of $2$ and $12$ .

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Step 5.4.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{12}$

Step 5.4.3.1.2

Cancel the common factors.

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Step 5.4.3.1.2.1

Factor $2$ out of $12$ .

$x = \frac{2 \cdot 1}{2 \cdot 6}$

Step 5.4.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 6}$

Step 5.4.3.1.2.3

Rewrite the expression.

$x = \frac{1}{6}$

Step 6

List all of the solutions.

$x = \frac{9}{2}, \frac{1}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{2}, \frac{1}{6}$

Decimal Form:

$x = 4.5, 0.1\overline{6}$

Mixed Number Form:

$x = 4 \frac{1}{2}, \frac{1}{6}$