Algebra Examples

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

Step 1

Simplify $\frac{1}{4} c - 3 (\frac{1}{2} c + 3)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Combine $\frac{1}{4}$ and $c$ .

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

Step 1.1.2

Combine $\frac{1}{2}$ and $c$ .

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

Step 1.1.3

Apply the distributive property.

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

Step 1.1.4

Combine $- 3$ and $\frac{c}{2}$ .

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

Step 1.1.5

Multiply $- 3$ by $3$ .

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

Step 1.1.6

Move the negative in front of the fraction.

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

Step 1.2

To write $- \frac{3 c}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{3 c}{2}$ by $\frac{2}{2}$ .

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

Step 1.3.2

Multiply $2$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

Simplify the numerator.

Tap for more steps...

Step 1.5.1.1

Factor $c$ out of $c - 3 c \cdot 2$ .

Tap for more steps...

Step 1.5.1.1.1

Raise $c$ to the power of $1$ .

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

Step 1.5.1.1.2

Factor $c$ out of $c^{1}$ .

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

Step 1.5.1.1.3

Factor $c$ out of $- 3 c \cdot 2$ .

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

Step 1.5.1.1.4

Factor $c$ out of $c \cdot 1 + c (- 3 \cdot 2)$ .

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

Step 1.5.1.2

Multiply $- 3$ by $2$ .

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

Step 1.5.1.3

Subtract $6$ from $1$ .

$\frac{c \cdot - 5}{4} - 9 = - \frac{3}{4} c$

Step 1.5.2

Move $- 5$ to the left of $c$ .

$\frac{- 5 \cdot c}{4} - 9 = - \frac{3}{4} c$

Step 1.5.3

Move the negative in front of the fraction.

$- \frac{5 c}{4} - 9 = - \frac{3}{4} c$

Step 2

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

Tap for more steps...

Step 2.1

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

$- \frac{5 c}{4} - 9 = - \frac{c \cdot 3}{4}$

Step 2.2

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

$- \frac{5 c}{4} - 9 = - \frac{3 c}{4}$

Step 3

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

Tap for more steps...

Step 3.1

Add $\frac{3 c}{4}$ to both sides of the equation.

$- \frac{5 c}{4} - 9 + \frac{3 c}{4} = 0$

Step 3.2

Combine the numerators over the common denominator.

$- 9 + \frac{- 5 c + 3 c}{4} = 0$

Step 3.3

Add $- 5 c$ and $3 c$ .

$- 9 + \frac{- 2 c}{4} = 0$

Step 3.4

Simplify each term.

Tap for more steps...

Step 3.4.1

Cancel the common factor of $- 2$ and $4$ .

Tap for more steps...

Step 3.4.1.1

Factor $2$ out of $- 2 c$ .

$- 9 + \frac{2 (- c)}{4} = 0$

Step 3.4.1.2

Cancel the common factors.

Tap for more steps...

Step 3.4.1.2.1

Factor $2$ out of $4$ .

$- 9 + \frac{2 (- c)}{2 (2)} = 0$

Step 3.4.1.2.2

Cancel the common factor.

$- 9 + \frac{2 (- c)}{2 \cdot 2} = 0$

Step 3.4.1.2.3

Rewrite the expression.

$- 9 + \frac{- c}{2} = 0$

Step 3.4.2

Move the negative in front of the fraction.

$- 9 - \frac{c}{2} = 0$

Step 4

Add $9$ to both sides of the equation.

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

Step 5

Multiply both sides of the equation by $- 2$ .

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

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $- 2 (- \frac{c}{2})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in $- \frac{c}{2}$ into the numerator.

$- 2 \frac{- c}{2} = - 2 \cdot 9$

Step 6.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 6.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- c}{2} = - 2 \cdot 9$

Step 6.1.1.1.4

Rewrite the expression.

$- - c = - 2 \cdot 9$

Step 6.1.1.2

Multiply.

Tap for more steps...

Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 c = - 2 \cdot 9$

Step 6.1.1.2.2

Multiply $c$ by $1$ .

$c = - 2 \cdot 9$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Multiply $- 2$ by $9$ .

$c = - 18$