Basic Math Examples

$| \frac{5 c - 4}{3 c - 5} | = 2$

Step 1

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

$\frac{5 c - 4}{3 c - 5} = \pm 2$

Step 2

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

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Step 2.1

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

$\frac{5 c - 4}{3 c - 5} = 2$

Step 2.2

Find the LCD of the terms in the equation.

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Step 2.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 c - 5, 1$

Step 2.2.2

Remove parentheses.

$3 c - 5, 1$

Step 2.2.3

The LCM of one and any expression is the expression.

$3 c - 5$

Step 2.3

Multiply each term in $\frac{5 c - 4}{3 c - 5} = 2$ by $3 c - 5$ to eliminate the fractions.

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Step 2.3.1

Multiply each term in $\frac{5 c - 4}{3 c - 5} = 2$ by $3 c - 5$ .

$\frac{5 c - 4}{3 c - 5} (3 c - 5) = 2 (3 c - 5)$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3 c - 5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 c - 4}{3 c - 5} (3 c - 5) = 2 (3 c - 5)$

Step 2.3.2.1.2

Rewrite the expression.

$5 c - 4 = 2 (3 c - 5)$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Apply the distributive property.

$5 c - 4 = 2 (3 c) + 2 \cdot - 5$

Step 2.3.3.2

Multiply.

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Step 2.3.3.2.1

Multiply $3$ by $2$ .

$5 c - 4 = 6 c + 2 \cdot - 5$

Step 2.3.3.2.2

Multiply $2$ by $- 5$ .

$5 c - 4 = 6 c - 10$

Step 2.4

Solve the equation.

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Step 2.4.1

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

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Step 2.4.1.1

Subtract $6 c$ from both sides of the equation.

$5 c - 4 - 6 c = - 10$

Step 2.4.1.2

Subtract $6 c$ from $5 c$ .

$- c - 4 = - 10$

Step 2.4.2

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

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Step 2.4.2.1

Add $4$ to both sides of the equation.

$- c = - 10 + 4$

Step 2.4.2.2

Add $- 10$ and $4$ .

$- c = - 6$

Step 2.4.3

Divide each term in $- c = - 6$ by $- 1$ and simplify.

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Step 2.4.3.1

Divide each term in $- c = - 6$ by $- 1$ .

$\frac{- c}{- 1} = \frac{- 6}{- 1}$

Step 2.4.3.2

Simplify the left side.

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Step 2.4.3.2.1

Dividing two negative values results in a positive value.

$\frac{c}{1} = \frac{- 6}{- 1}$

Step 2.4.3.2.2

Divide $c$ by $1$ .

$c = \frac{- 6}{- 1}$

Step 2.4.3.3

Simplify the right side.

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Step 2.4.3.3.1

Divide $- 6$ by $- 1$ .

$c = 6$

Step 2.5

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

$\frac{5 c - 4}{3 c - 5} = - 2$

Step 2.6

Find the LCD of the terms in the equation.

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Step 2.6.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 c - 5, 1$

Step 2.6.2

Remove parentheses.

$3 c - 5, 1$

Step 2.6.3

The LCM of one and any expression is the expression.

$3 c - 5$

Step 2.7

Multiply each term in $\frac{5 c - 4}{3 c - 5} = - 2$ by $3 c - 5$ to eliminate the fractions.

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Step 2.7.1

Multiply each term in $\frac{5 c - 4}{3 c - 5} = - 2$ by $3 c - 5$ .

$\frac{5 c - 4}{3 c - 5} (3 c - 5) = - 2 (3 c - 5)$

Step 2.7.2

Simplify the left side.

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Step 2.7.2.1

Cancel the common factor of $3 c - 5$ .

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Step 2.7.2.1.1

Cancel the common factor.

$\frac{5 c - 4}{3 c - 5} (3 c - 5) = - 2 (3 c - 5)$

Step 2.7.2.1.2

Rewrite the expression.

$5 c - 4 = - 2 (3 c - 5)$

Step 2.7.3

Simplify the right side.

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Step 2.7.3.1

Apply the distributive property.

$5 c - 4 = - 2 (3 c) - 2 \cdot - 5$

Step 2.7.3.2

Multiply.

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Step 2.7.3.2.1

Multiply $3$ by $- 2$ .

$5 c - 4 = - 6 c - 2 \cdot - 5$

Step 2.7.3.2.2

Multiply $- 2$ by $- 5$ .

$5 c - 4 = - 6 c + 10$

Step 2.8

Solve the equation.

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Step 2.8.1

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

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Step 2.8.1.1

Add $6 c$ to both sides of the equation.

$5 c - 4 + 6 c = 10$

Step 2.8.1.2

Add $5 c$ and $6 c$ .

$11 c - 4 = 10$

Step 2.8.2

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

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Step 2.8.2.1

Add $4$ to both sides of the equation.

$11 c = 10 + 4$

Step 2.8.2.2

Add $10$ and $4$ .

$11 c = 14$

Step 2.8.3

Divide each term in $11 c = 14$ by $11$ and simplify.

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Step 2.8.3.1

Divide each term in $11 c = 14$ by $11$ .

$\frac{11 c}{11} = \frac{14}{11}$

Step 2.8.3.2

Simplify the left side.

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Step 2.8.3.2.1

Cancel the common factor of $11$ .

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Step 2.8.3.2.1.1

Cancel the common factor.

$\frac{11 c}{11} = \frac{14}{11}$

Step 2.8.3.2.1.2

Divide $c$ by $1$ .

$c = \frac{14}{11}$

Step 2.9

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

$c = 6, \frac{14}{11}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$c = 6, \frac{14}{11}$

Decimal Form:

$c = 6, 1.\overline{27}$

Mixed Number Form:

$c = 6, 1 \frac{3}{11}$