Algebra Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Combine $c$ and $\frac{3}{4}$ .

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

Step 1.1.3

Cancel the common factor of $4$ .

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Step 1.1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$- 3 - \frac{c \cdot 3}{4} + \frac{- 3}{4} \cdot - 4 = \frac{5}{4}$

Step 1.1.3.2

Factor $4$ out of $- 4$ .

$- 3 - \frac{c \cdot 3}{4} + \frac{- 3}{4} \cdot (4 (- 1)) = \frac{5}{4}$

Step 1.1.3.3

Cancel the common factor.

$- 3 - \frac{c \cdot 3}{4} + \frac{- 3}{4} \cdot (4 \cdot - 1) = \frac{5}{4}$

Step 1.1.3.4

Rewrite the expression.

$- 3 - \frac{c \cdot 3}{4} - 3 \cdot - 1 = \frac{5}{4}$

Step 1.1.4

Multiply $- 3$ by $- 1$ .

$- 3 - \frac{c \cdot 3}{4} + 3 = \frac{5}{4}$

Step 1.1.5

Move $3$ to the left of $c$ .

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

Step 1.2

Combine the opposite terms in $- 3 - \frac{3 c}{4} + 3$ .

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Step 1.2.1

Add $- 3$ and $3$ .

$- \frac{3 c}{4} + 0 = \frac{5}{4}$

Step 1.2.2

Add $- \frac{3 c}{4}$ and $0$ .

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

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 3 c = 5$

Step 3

Divide each term in $- 3 c = 5$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 c = 5$ by $- 3$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $c$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$c = - 1.\overline{6}$

Mixed Number Form:

$c = - 1 \frac{2}{3}$