Algebra Examples

$\frac{3}{8} f + \frac{1}{2} = 6 (\frac{1}{16} f - 3)$

Step 1

Combine $\frac{3}{8}$ and $f$ .

$\frac{3 f}{8} + \frac{1}{2} = 6 (\frac{1}{16} f - 3)$

Step 2

Simplify $6 (\frac{1}{16} f - 3)$ .

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Step 2.1

Combine $\frac{1}{16}$ and $f$ .

$\frac{3 f}{8} + \frac{1}{2} = 6 (\frac{f}{16} - 3)$

Step 2.2

Apply the distributive property.

$\frac{3 f}{8} + \frac{1}{2} = 6 \frac{f}{16} + 6 \cdot - 3$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $6$ .

$\frac{3 f}{8} + \frac{1}{2} = 2 (3) \frac{f}{16} + 6 \cdot - 3$

Step 2.3.2

Factor $2$ out of $16$ .

$\frac{3 f}{8} + \frac{1}{2} = 2 \cdot 3 \frac{f}{2 \cdot 8} + 6 \cdot - 3$

Step 2.3.3

Cancel the common factor.

$\frac{3 f}{8} + \frac{1}{2} = 2 \cdot 3 \frac{f}{2 \cdot 8} + 6 \cdot - 3$

Step 2.3.4

Rewrite the expression.

$\frac{3 f}{8} + \frac{1}{2} = 3 \frac{f}{8} + 6 \cdot - 3$

Step 2.4

Combine $3$ and $\frac{f}{8}$ .

$\frac{3 f}{8} + \frac{1}{2} = \frac{3 f}{8} + 6 \cdot - 3$

Step 2.5

Multiply $6$ by $- 3$ .

$\frac{3 f}{8} + \frac{1}{2} = \frac{3 f}{8} - 18$

Step 3

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

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Step 3.1

Subtract $\frac{3 f}{8}$ from both sides of the equation.

$\frac{3 f}{8} + \frac{1}{2} - \frac{3 f}{8} = - 18$

Step 3.2

Combine the opposite terms in $\frac{3 f}{8} + \frac{1}{2} - \frac{3 f}{8}$ .

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Step 3.2.1

Subtract $\frac{3 f}{8}$ from $\frac{3 f}{8}$ .

$0 + \frac{1}{2} = - 18$

Step 3.2.2

Add $0$ and $\frac{1}{2}$ .

$\frac{1}{2} = - 18$

Step 4

Since $\frac{1}{2} \neq - 18$ , there are no solutions.

No solution