Algebra Examples

\frac{3}{5} (10 - 5 c) = \frac{3}{2} - \frac{5}{3} c

$\frac{3}{5} (10 - 5 c) = \frac{3}{2} - \frac{5}{3} c$

Step 1

Simplify

\frac{3}{5} \cdot (10 - 5 c)

$\frac{3}{5} \cdot (10 - 5 c)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{5} \cdot (10 - 5 c) = \frac{3}{2} - \frac{5}{3} c$

Step 1.2

Simplify by adding zeros.

$\frac{3}{5} \cdot (10 - 5 c) = \frac{3}{2} - \frac{5}{3} c$

Step 1.3

Apply the distributive property.

$\frac{3}{5} \cdot 10 + \frac{3}{5} (- 5 c) = \frac{3}{2} - \frac{5}{3} c$

Step 1.4

Cancel the common factor of

$5$ .

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Step 1.4.1

Factor

$5$ out of

$10$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

Multiply

$3$ by

$2$ .

$6 + \frac{3}{5} (- 5 c) = \frac{3}{2} - \frac{5}{3} c$

Step 1.6

Cancel the common factor of

$5$ .

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Step 1.6.1

Factor

$5$ out of

$- 5 c$ .

$6 + \frac{3}{5} (5 (- c)) = \frac{3}{2} - \frac{5}{3} c$

Step 1.6.2

Cancel the common factor.

$6 + \frac{3}{5} (5 (- c)) = \frac{3}{2} - \frac{5}{3} c$

Step 1.6.3

Rewrite the expression.

$6 + 3 (- c) = \frac{3}{2} - \frac{5}{3} c$

Step 1.7

Multiply

$- 1$ by

$3$ .

$6 - 3 c = \frac{3}{2} - \frac{5}{3} c$

Step 2

Simplify each term.

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Step 2.1

Combine

$c$ and

$\frac{5}{3}$ .

$6 - 3 c = \frac{3}{2} - \frac{c \cdot 5}{3}$

Step 2.2

Move

$5$ to the left of

$c$ .

$6 - 3 c = \frac{3}{2} - \frac{5 c}{3}$

Step 3

Move all terms containing

$c$ to the left side of the equation.

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Step 3.1

Add

$\frac{5 c}{3}$ to both sides of the equation.

$6 - 3 c + \frac{5 c}{3} = \frac{3}{2}$

Step 3.2

To write

$- 3 c$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$6 - 3 c \cdot \frac{3}{3} + \frac{5 c}{3} = \frac{3}{2}$

Step 3.3

Combine

$- 3 c$ and

$\frac{3}{3}$ .

$6 + \frac{- 3 c \cdot 3}{3} + \frac{5 c}{3} = \frac{3}{2}$

Step 3.4

Combine the numerators over the common denominator.

$6 + \frac{- 3 c \cdot 3 + 5 c}{3} = \frac{3}{2}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor

$c$ out of

$- 3 c \cdot 3 + 5 c$ .

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Step 3.5.1.1.1

Factor

$c$ out of

$- 3 c \cdot 3$ .

$6 + \frac{c (- 3 \cdot 3) + 5 c}{3} = \frac{3}{2}$

Step 3.5.1.1.2

Factor

$c$ out of

$5 c$ .

$6 + \frac{c (- 3 \cdot 3) + c \cdot 5}{3} = \frac{3}{2}$

Step 3.5.1.1.3

Factor

$c$ out of

$c (- 3 \cdot 3) + c \cdot 5$ .

$6 + \frac{c (- 3 \cdot 3 + 5)}{3} = \frac{3}{2}$

Step 3.5.1.2

Multiply

$- 3$ by

$3$ .

$6 + \frac{c (- 9 + 5)}{3} = \frac{3}{2}$

Step 3.5.1.3

Add

$- 9$ and

$5$ .

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

Step 3.5.2

Move

$- 4$ to the left of

$c$ .

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

Step 3.5.3

Move the negative in front of the fraction.

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

Step 4

Move all terms not containing

$c$ to the right side of the equation.

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Step 4.1

Subtract

$6$ from both sides of the equation.

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

Step 4.2

To write

$- 6$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$- \frac{4 c}{3} = \frac{3}{2} - 6 \cdot \frac{2}{2}$

Step 4.3

Combine

$- 6$ and

$\frac{2}{2}$ .

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

Step 4.4

Combine the numerators over the common denominator.

$- \frac{4 c}{3} = \frac{3 - 6 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply

$- 6$ by

$2$ .

$- \frac{4 c}{3} = \frac{3 - 12}{2}$

Step 4.5.2

Subtract

$12$ from

$3$ .

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

Step 4.6

Move the negative in front of the fraction.

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

Step 5

Multiply both sides of the equation by

$- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 c}{3}) = - \frac{3}{4} (- \frac{9}{2})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify

$- \frac{3}{4} (- \frac{4 c}{3})$ .

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Step 6.1.1.1

Cancel the common factor of

$3$ .

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Step 6.1.1.1.1

Move the leading negative in

$- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 c}{3}) = - \frac{3}{4} (- \frac{9}{2})$

Step 6.1.1.1.2

Move the leading negative in

$- \frac{4 c}{3}$ into the numerator.

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

Step 6.1.1.1.3

Factor

$3$ out of

$- 3$ .

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

Step 6.1.1.1.4

Cancel the common factor.

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

Step 6.1.1.1.5

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of

$4$ .

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Step 6.1.1.2.1

Factor

$4$ out of

$- 4 c$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

$- - c = - \frac{3}{4} (- \frac{9}{2})$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply

$- 1$ by

$- 1$ .

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

Step 6.1.1.3.2

Multiply

$c$ by

$1$ .

$c = - \frac{3}{4} (- \frac{9}{2})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply

$- \frac{3}{4} (- \frac{9}{2})$ .

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Step 6.2.1.1

Multiply

$- 1$ by

$- 1$ .

$c = 1 (\frac{3}{4}) \frac{9}{2}$

Step 6.2.1.2

Multiply

$\frac{3}{4}$ by

$1$ .

$c = \frac{3}{4} \cdot \frac{9}{2}$

Step 6.2.1.3

Multiply

$\frac{3}{4}$ by

$\frac{9}{2}$ .

$c = \frac{3 \cdot 9}{4 \cdot 2}$

Step 6.2.1.4

Multiply

$3$ by

$9$ .

$c = \frac{27}{4 \cdot 2}$

Step 6.2.1.5

Multiply

$4$ by

$2$ .

$c = \frac{27}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$c = \frac{27}{8}$

Decimal Form:

$c = 3.375$

Mixed Number Form:

$c = 3 \frac{3}{8}$