Algebra Examples

$12 + \frac{3}{2} s - \frac{1}{2} - \frac{3}{4} s = \frac{5}{4} s$

Step 1

Simplify $12 + \frac{3}{2} s - \frac{1}{2} - \frac{3}{4} s$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$12 + \frac{3 s}{2} - \frac{1}{2} - \frac{3}{4} s = \frac{5}{4} s$

Step 1.1.2

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

$12 + \frac{3 s}{2} - \frac{1}{2} - \frac{s \cdot 3}{4} = \frac{5}{4} s$

Step 1.1.3

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

$12 + \frac{3 s}{2} - \frac{1}{2} - \frac{3 s}{4} = \frac{5}{4} s$

Step 1.2

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 s}{2} + 12 \cdot \frac{2}{2} - \frac{1}{2} - \frac{3 s}{4} = \frac{5}{4} s$

Step 1.3

Combine $12$ and $\frac{2}{2}$ .

$\frac{3 s}{2} + \frac{12 \cdot 2}{2} - \frac{1}{2} - \frac{3 s}{4} = \frac{5}{4} s$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 s}{2} + \frac{12 \cdot 2 - 1}{2} - \frac{3 s}{4} = \frac{5}{4} s$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $12$ by $2$ .

$\frac{3 s}{2} + \frac{24 - 1}{2} - \frac{3 s}{4} = \frac{5}{4} s$

Step 1.5.2

Subtract $1$ from $24$ .

$\frac{3 s}{2} + \frac{23}{2} - \frac{3 s}{4} = \frac{5}{4} s$

Step 1.6

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

$\frac{3 s}{2} \cdot \frac{2}{2} - \frac{3 s}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.7

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

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Step 1.7.1

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

$\frac{3 s \cdot 2}{2 \cdot 2} - \frac{3 s}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.7.2

Multiply $2$ by $2$ .

$\frac{3 s \cdot 2}{4} - \frac{3 s}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.8

Combine the numerators over the common denominator.

$\frac{3 s \cdot 2 - 3 s}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.9

Simplify the numerator.

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Step 1.9.1

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

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Step 1.9.1.1

Factor $3 s$ out of $3 s \cdot 2$ .

$\frac{3 s (2) - 3 s}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.9.1.2

Factor $3 s$ out of $- 3 s$ .

$\frac{3 s (2) + 3 s (- 1)}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.9.1.3

Factor $3 s$ out of $3 s (2) + 3 s (- 1)$ .

$\frac{3 s (2 - 1)}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.9.2

Subtract $1$ from $2$ .

$\frac{3 s \cdot 1}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 1.9.3

Multiply $3$ by $1$ .

$\frac{3 s}{4} + \frac{23}{2} = \frac{5}{4} s$

Step 2

Combine $\frac{5}{4}$ and $s$ .

$\frac{3 s}{4} + \frac{23}{2} = \frac{5 s}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{5 s}{4}$ from both sides of the equation.

$\frac{3 s}{4} + \frac{23}{2} - \frac{5 s}{4} = 0$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 s - 5 s}{4} + \frac{23}{2} = 0$

Step 3.3

Subtract $5 s$ from $3 s$ .

$\frac{- 2 s}{4} + \frac{23}{2} = 0$

Step 3.4

Simplify each term.

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Step 3.4.1

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

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Step 3.4.1.1

Factor $2$ out of $- 2 s$ .

$\frac{2 (- s)}{4} + \frac{23}{2} = 0$

Step 3.4.1.2

Cancel the common factors.

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Step 3.4.1.2.1

Factor $2$ out of $4$ .

$\frac{2 (- s)}{2 (2)} + \frac{23}{2} = 0$

Step 3.4.1.2.2

Cancel the common factor.

$\frac{2 (- s)}{2 \cdot 2} + \frac{23}{2} = 0$

Step 3.4.1.2.3

Rewrite the expression.

$\frac{- s}{2} + \frac{23}{2} = 0$

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{s}{2} + \frac{23}{2} = 0$

Step 4

Subtract $\frac{23}{2}$ from both sides of the equation.

$- \frac{s}{2} = - \frac{23}{2}$

Step 5

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

$- s = - 23$

Step 6

Divide each term in $- s = - 23$ by $- 1$ and simplify.

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Step 6.1

Divide each term in $- s = - 23$ by $- 1$ .

$\frac{- s}{- 1} = \frac{- 23}{- 1}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Dividing two negative values results in a positive value.

$\frac{s}{1} = \frac{- 23}{- 1}$

Step 6.2.2

Divide $s$ by $1$ .

$s = \frac{- 23}{- 1}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 23$ by $- 1$ .

$s = 23$