Algebra Examples

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

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.

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

Step 2

Simplify $\frac{1}{4} \cdot (3 - c) + \frac{1}{8} c$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Combine $\frac{1}{4}$ and $3$ .

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

Step 2.1.3

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

$\frac{3}{4} - \frac{c}{4} + \frac{1}{8} c = 4 - \frac{1}{2} c$

Step 2.1.4

Combine $\frac{1}{8}$ and $c$ .

$\frac{3}{4} - \frac{c}{4} + \frac{c}{8} = 4 - \frac{1}{2} c$

Step 2.2

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

$\frac{3}{4} - \frac{c}{4} \cdot \frac{2}{2} + \frac{c}{8} = 4 - \frac{1}{2} c$

Step 2.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.1

Multiply $\frac{c}{4}$ by $\frac{2}{2}$ .

$\frac{3}{4} - \frac{c \cdot 2}{4 \cdot 2} + \frac{c}{8} = 4 - \frac{1}{2} c$

Step 2.3.2

Multiply $4$ by $2$ .

$\frac{3}{4} - \frac{c \cdot 2}{8} + \frac{c}{8} = 4 - \frac{1}{2} c$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3}{4} + \frac{- c \cdot 2 + c}{8} = 4 - \frac{1}{2} c$

Step 2.5

Simplify each term.

Tap for more steps...

Step 2.5.1

Simplify the numerator.

Tap for more steps...

Step 2.5.1.1

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

Tap for more steps...

Step 2.5.1.1.1

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

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

Step 2.5.1.1.2

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

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

Step 2.5.1.1.3

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

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

Step 2.5.1.1.4

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

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

Step 2.5.1.2

Multiply $- 1$ by $2$ .

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

Step 2.5.1.3

Add $- 2$ and $1$ .

$\frac{3}{4} + \frac{c \cdot - 1}{8} = 4 - \frac{1}{2} c$

Step 2.5.2

Move $- 1$ to the left of $c$ .

$\frac{3}{4} + \frac{- 1 \cdot c}{8} = 4 - \frac{1}{2} c$

Step 2.5.3

Move the negative in front of the fraction.

$\frac{3}{4} - \frac{c}{8} = 4 - \frac{1}{2} c$

Step 3

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

$\frac{3}{4} - \frac{c}{8} = 4 - \frac{c}{2}$

Step 4

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

Tap for more steps...

Step 4.1

Add $\frac{c}{2}$ to both sides of the equation.

$\frac{3}{4} - \frac{c}{8} + \frac{c}{2} = 4$

Step 4.2

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

$\frac{3}{4} - \frac{c}{8} + \frac{c}{2} \cdot \frac{4}{4} = 4$

Step 4.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.3.1

Multiply $\frac{c}{2}$ by $\frac{4}{4}$ .

$\frac{3}{4} - \frac{c}{8} + \frac{c \cdot 4}{2 \cdot 4} = 4$

Step 4.3.2

Multiply $2$ by $4$ .

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Add $- c$ and $c \cdot 4$ .

Tap for more steps...

Step 4.5.1

Reorder $c$ and $4$ .

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

Step 4.5.2

Add $- c$ and $4 \cdot c$ .

$\frac{3}{4} + \frac{3 c}{8} = 4$

Step 5

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

Tap for more steps...

Step 5.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$\frac{3 c}{8} = 4 - \frac{3}{4}$

Step 5.2

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

$\frac{3 c}{8} = 4 \cdot \frac{4}{4} - \frac{3}{4}$

Step 5.3

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

$\frac{3 c}{8} = \frac{4 \cdot 4}{4} - \frac{3}{4}$

Step 5.4

Combine the numerators over the common denominator.

$\frac{3 c}{8} = \frac{4 \cdot 4 - 3}{4}$

Step 5.5

Simplify the numerator.

Tap for more steps...

Step 5.5.1

Multiply $4$ by $4$ .

$\frac{3 c}{8} = \frac{16 - 3}{4}$

Step 5.5.2

Subtract $3$ from $16$ .

$\frac{3 c}{8} = \frac{13}{4}$

Step 6

Multiply both sides of the equation by $\frac{8}{3}$ .

$\frac{8}{3} \cdot \frac{3 c}{8} = \frac{8}{3} \cdot \frac{13}{4}$

Step 7

Simplify both sides of the equation.

Tap for more steps...

Step 7.1

Simplify the left side.

Tap for more steps...

Step 7.1.1

Simplify $\frac{8}{3} \cdot \frac{3 c}{8}$ .

Tap for more steps...

Step 7.1.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 7.1.1.1.1

Cancel the common factor.

$\frac{8}{3} \cdot \frac{3 c}{8} = \frac{8}{3} \cdot \frac{13}{4}$

Step 7.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 c) = \frac{8}{3} \cdot \frac{13}{4}$

Step 7.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.1.1.2.1

Factor $3$ out of $3 c$ .

$\frac{1}{3} (3 (c)) = \frac{8}{3} \cdot \frac{13}{4}$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 c) = \frac{8}{3} \cdot \frac{13}{4}$

Step 7.1.1.2.3

Rewrite the expression.

$c = \frac{8}{3} \cdot \frac{13}{4}$

Step 7.2

Simplify the right side.

Tap for more steps...

Step 7.2.1

Simplify $\frac{8}{3} \cdot \frac{13}{4}$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 7.2.1.1.1

Factor $4$ out of $8$ .

$c = \frac{4 (2)}{3} \cdot \frac{13}{4}$

Step 7.2.1.1.2

Cancel the common factor.

$c = \frac{4 \cdot 2}{3} \cdot \frac{13}{4}$

Step 7.2.1.1.3

Rewrite the expression.

$c = \frac{2}{3} \cdot 13$

Step 7.2.1.2

Combine $\frac{2}{3}$ and $13$ .

$c = \frac{2 \cdot 13}{3}$

Step 7.2.1.3

Multiply $2$ by $13$ .

$c = \frac{26}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$c = \frac{26}{3}$

Decimal Form:

$c = 8.\overline{6}$

Mixed Number Form:

$c = 8 \frac{2}{3}$