Algebra Examples

$\frac{2 c - 1}{9} + \frac{c}{4} = \frac{c + 3}{6}$

Step 1

Multiply both sides by $6$ .

$(\frac{2 c - 1}{9} + \frac{c}{4}) \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{2 c - 1}{9} + \frac{c}{4}) \cdot 6$ .

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Step 2.1.1.1

To write $\frac{2 c - 1}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{2 c - 1}{9} \cdot \frac{4}{4} + \frac{c}{4}) \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.2

To write $\frac{c}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$(\frac{2 c - 1}{9} \cdot \frac{4}{4} + \frac{c}{4} \cdot \frac{9}{9}) \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.3.1

Multiply $\frac{2 c - 1}{9}$ by $\frac{4}{4}$ .

$(\frac{(2 c - 1) \cdot 4}{9 \cdot 4} + \frac{c}{4} \cdot \frac{9}{9}) \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.3.2

Multiply $9$ by $4$ .

$(\frac{(2 c - 1) \cdot 4}{36} + \frac{c}{4} \cdot \frac{9}{9}) \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.3.3

Multiply $\frac{c}{4}$ by $\frac{9}{9}$ .

$(\frac{(2 c - 1) \cdot 4}{36} + \frac{c \cdot 9}{4 \cdot 9}) \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.3.4

Multiply $4$ by $9$ .

$(\frac{(2 c - 1) \cdot 4}{36} + \frac{c \cdot 9}{36}) \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{(2 c - 1) \cdot 4 + c \cdot 9}{36} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Apply the distributive property.

$\frac{2 c \cdot 4 - 1 \cdot 4 + c \cdot 9}{36} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.5.2

Multiply $4$ by $2$ .

$\frac{8 c - 1 \cdot 4 + c \cdot 9}{36} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.5.3

Multiply $- 1$ by $4$ .

$\frac{8 c - 4 + c \cdot 9}{36} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.5.4

Move $9$ to the left of $c$ .

$\frac{8 c - 4 + 9 \cdot c}{36} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.5.5

Add $8 c$ and $9 c$ .

$\frac{17 c - 4}{36} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.6

Cancel the common factor of $6$ .

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Step 2.1.1.6.1

Factor $6$ out of $36$ .

$\frac{17 c - 4}{6 (6)} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{17 c - 4}{6 \cdot 6} \cdot 6 = \frac{c + 3}{6} \cdot 6$

Step 2.1.1.6.3

Rewrite the expression.

$\frac{17 c - 4}{6} = \frac{c + 3}{6} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{17 c - 4}{6} = \frac{c + 3}{6} \cdot 6$

Step 2.2.1.2

Rewrite the expression.

$\frac{17 c - 4}{6} = c + 3$

Step 3

Solve for $c$ .

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Step 3.1

Multiply both sides by $6$ .

$\frac{17 c - 4}{6} \cdot 6 = (c + 3) \cdot 6$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $6$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{17 c - 4}{6} \cdot 6 = (c + 3) \cdot 6$

Step 3.2.1.1.2

Rewrite the expression.

$17 c - 4 = (c + 3) \cdot 6$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(c + 3) \cdot 6$ .

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Step 3.2.2.1.1

Apply the distributive property.

$17 c - 4 = c \cdot 6 + 3 \cdot 6$

Step 3.2.2.1.2

Simplify the expression.

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Step 3.2.2.1.2.1

Move $6$ to the left of $c$ .

$17 c - 4 = 6 \cdot c + 3 \cdot 6$

Step 3.2.2.1.2.2

Multiply $3$ by $6$ .

$17 c - 4 = 6 c + 18$

Step 3.3

Solve for $c$ .

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Step 3.3.1

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

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Step 3.3.1.1

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

$17 c - 4 - 6 c = 18$

Step 3.3.1.2

Subtract $6 c$ from $17 c$ .

$11 c - 4 = 18$

Step 3.3.2

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

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Step 3.3.2.1

Add $4$ to both sides of the equation.

$11 c = 18 + 4$

Step 3.3.2.2

Add $18$ and $4$ .

$11 c = 22$

Step 3.3.3

Divide each term in $11 c = 22$ by $11$ and simplify.

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Step 3.3.3.1

Divide each term in $11 c = 22$ by $11$ .

$\frac{11 c}{11} = \frac{22}{11}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $11$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{11 c}{11} = \frac{22}{11}$

Step 3.3.3.2.1.2

Divide $c$ by $1$ .

$c = \frac{22}{11}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $22$ by $11$ .

$c = 2$