Finite Math Examples

$| 5 x - 1 | = | 10 x + 17 |$

Step 1

Rewrite the equation as $| 10 x + 17 | = | 5 x - 1 |$ .

$| 10 x + 17 | = | 5 x - 1 |$

Step 2

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

$10 x + 17 = 5 x - 1$

$10 x + 17 = - (5 x - 1)$

$- (10 x + 17) = 5 x - 1$

$- (10 x + 17) = - (5 x - 1)$

Step 3

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

$10 x + 17 = 5 x - 1$

$10 x + 17 = - (5 x - 1)$

Step 4

Solve $10 x + 17 = 5 x - 1$ 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 $5 x$ from both sides of the equation.

$10 x + 17 - 5 x = - 1$

Step 4.1.2

Subtract $5 x$ from $10 x$ .

$5 x + 17 = - 1$

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 $17$ from both sides of the equation.

$5 x = - 1 - 17$

Step 4.2.2

Subtract $17$ from $- 1$ .

$5 x = - 18$

Step 4.3

Divide each term in $5 x = - 18$ by $5$ and simplify.

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Step 4.3.1

Divide each term in $5 x = - 18$ by $5$ .

$\frac{5 x}{5} = \frac{- 18}{5}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $5$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 18}{5}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 18}{5}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$x = - \frac{18}{5}$

Step 5

Solve $10 x + 17 = - (5 x - 1)$ for $x$ .

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Step 5.1

Simplify $- (5 x - 1)$ .

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Step 5.1.1

Rewrite.

$10 x + 17 = 0 + 0 - (5 x - 1)$

Step 5.1.2

Simplify by adding zeros.

$10 x + 17 = - (5 x - 1)$

Step 5.1.3

Apply the distributive property.

$10 x + 17 = - (5 x) - - 1$

Step 5.1.4

Multiply.

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Step 5.1.4.1

Multiply $5$ by $- 1$ .

$10 x + 17 = - 5 x - - 1$

Step 5.1.4.2

Multiply $- 1$ by $- 1$ .

$10 x + 17 = - 5 x + 1$

Step 5.2

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

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Step 5.2.1

Add $5 x$ to both sides of the equation.

$10 x + 17 + 5 x = 1$

Step 5.2.2

Add $10 x$ and $5 x$ .

$15 x + 17 = 1$

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 $17$ from both sides of the equation.

$15 x = 1 - 17$

Step 5.3.2

Subtract $17$ from $1$ .

$15 x = - 16$

Step 5.4

Divide each term in $15 x = - 16$ by $15$ and simplify.

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Step 5.4.1

Divide each term in $15 x = - 16$ by $15$ .

$\frac{15 x}{15} = \frac{- 16}{15}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $15$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{15 x}{15} = \frac{- 16}{15}$

Step 5.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 16}{15}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Move the negative in front of the fraction.

$x = - \frac{16}{15}$

Step 6

List all of the solutions.

$x = - \frac{18}{5}, - \frac{16}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{18}{5}, - \frac{16}{15}$

Decimal Form:

$x = - 3.6, - 1.0\overline{6}$

Mixed Number Form:

$x = - 3 \frac{3}{5}, - 1 \frac{1}{15}$