Algebra Examples

$4 c + 9 = \frac{8 c + 1 - (2 c - 11)}{3}$

Step 1

Since $c$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{8 c + 1 - (2 c - 11)}{3} = 4 c + 9$

Step 2

Multiply both sides by $3$ .

$\frac{8 c + 1 - (2 c - 11)}{3} \cdot 3 = (4 c + 9) \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{8 c + 1 - (2 c - 11)}{3} \cdot 3$ .

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Step 3.1.1.1

Simplify the numerator.

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Step 3.1.1.1.1

Apply the distributive property.

$\frac{8 c + 1 - (2 c) - - 11}{3} \cdot 3 = (4 c + 9) \cdot 3$

Step 3.1.1.1.2

Multiply $2$ by $- 1$ .

$\frac{8 c + 1 - 2 c - - 11}{3} \cdot 3 = (4 c + 9) \cdot 3$

Step 3.1.1.1.3

Multiply $- 1$ by $- 11$ .

$\frac{8 c + 1 - 2 c + 11}{3} \cdot 3 = (4 c + 9) \cdot 3$

Step 3.1.1.1.4

Subtract $2 c$ from $8 c$ .

$\frac{6 c + 1 + 11}{3} \cdot 3 = (4 c + 9) \cdot 3$

Step 3.1.1.1.5

Add $1$ and $11$ .

$\frac{6 c + 12}{3} \cdot 3 = (4 c + 9) \cdot 3$

Step 3.1.1.1.6

Factor $6$ out of $6 c + 12$ .

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Step 3.1.1.1.6.1

Factor $6$ out of $6 c$ .

$\frac{6 (c) + 12}{3} \cdot 3 = (4 c + 9) \cdot 3$

Step 3.1.1.1.6.2

Factor $6$ out of $12$ .

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

Step 3.1.1.1.6.3

Factor $6$ out of $6 c + 6 \cdot 2$ .

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

Step 3.1.1.2

Simplify terms.

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Step 3.1.1.2.1

Cancel the common factor of $3$ .

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Step 3.1.1.2.1.1

Cancel the common factor.

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

Step 3.1.1.2.1.2

Rewrite the expression.

$6 (c + 2) = (4 c + 9) \cdot 3$

Step 3.1.1.2.2

Apply the distributive property.

$6 c + 6 \cdot 2 = (4 c + 9) \cdot 3$

Step 3.1.1.2.3

Multiply $6$ by $2$ .

$6 c + 12 = (4 c + 9) \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(4 c + 9) \cdot 3$ .

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Step 3.2.1.1

Apply the distributive property.

$6 c + 12 = 4 c \cdot 3 + 9 \cdot 3$

Step 3.2.1.2

Multiply.

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Step 3.2.1.2.1

Multiply $3$ by $4$ .

$6 c + 12 = 12 c + 9 \cdot 3$

Step 3.2.1.2.2

Multiply $9$ by $3$ .

$6 c + 12 = 12 c + 27$

Step 4

Solve for $c$ .

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Step 4.1

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

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Step 4.1.1

Subtract $12 c$ from both sides of the equation.

$6 c + 12 - 12 c = 27$

Step 4.1.2

Subtract $12 c$ from $6 c$ .

$- 6 c + 12 = 27$

Step 4.2

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

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Step 4.2.1

Subtract $12$ from both sides of the equation.

$- 6 c = 27 - 12$

Step 4.2.2

Subtract $12$ from $27$ .

$- 6 c = 15$

Step 4.3

Divide each term in $- 6 c = 15$ by $- 6$ and simplify.

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Step 4.3.1

Divide each term in $- 6 c = 15$ by $- 6$ .

$\frac{- 6 c}{- 6} = \frac{15}{- 6}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 6$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 6 c}{- 6} = \frac{15}{- 6}$

Step 4.3.2.1.2

Divide $c$ by $1$ .

$c = \frac{15}{- 6}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $15$ and $- 6$ .

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Step 4.3.3.1.1

Factor $3$ out of $15$ .

$c = \frac{3 (5)}{- 6}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $3$ out of $- 6$ .

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

Step 4.3.3.1.2.2

Cancel the common factor.

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

Step 4.3.3.1.2.3

Rewrite the expression.

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

Step 4.3.3.2

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$c = - 2.5$

Mixed Number Form:

$c = - 2 \frac{1}{2}$