Basic Math Examples

$12 = 10 - \frac{3}{2 s - (- 4)}$

Step 1

Rewrite the equation as $10 - \frac{3}{2 s - (- 4)} = 12$ .

$10 - \frac{3}{2 s - (- 4)} = 12$

Step 2

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

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Step 2.1

Subtract $10$ from both sides of the equation.

$- \frac{3}{2 s - (- 4)} = 12 - 10$

Step 2.2

Subtract $10$ from $12$ .

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

Step 3

Factor each term.

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Step 3.1

Multiply $- 1$ by $- 4$ .

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

Step 3.2

Factor $2$ out of $2 s + 4$ .

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Step 3.2.1

Factor $2$ out of $2 s$ .

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

Step 3.2.2

Factor $2$ out of $4$ .

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

Step 3.2.3

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

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

Step 4

Find the LCD of the terms in the equation.

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Step 4.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 (s + 2), 1$

Step 4.2

The LCM of one and any expression is the expression.

$2 (s + 2)$

Step 5

Multiply each term in $- \frac{3}{2 (s + 2)} = 2$ by $2 (s + 2)$ to eliminate the fractions.

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Step 5.1

Multiply each term in $- \frac{3}{2 (s + 2)} = 2$ by $2 (s + 2)$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2 (s + 2)$ .

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Step 5.2.1.1

Move the leading negative in $- \frac{3}{2 (s + 2)}$ into the numerator.

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

Step 5.2.1.2

Cancel the common factor.

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

Step 5.2.1.3

Rewrite the expression.

$- 3 = 2 (2 (s + 2))$

Step 5.3

Simplify the right side.

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Step 5.3.1

Apply the distributive property.

$- 3 = 2 (2 s + 2 \cdot 2)$

Step 5.3.2

Multiply $2$ by $2$ .

$- 3 = 2 (2 s + 4)$

Step 5.3.3

Apply the distributive property.

$- 3 = 2 (2 s) + 2 \cdot 4$

Step 5.3.4

Multiply.

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Step 5.3.4.1

Multiply $2$ by $2$ .

$- 3 = 4 s + 2 \cdot 4$

Step 5.3.4.2

Multiply $2$ by $4$ .

$- 3 = 4 s + 8$

Step 6

Solve the equation.

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Step 6.1

Rewrite the equation as $4 s + 8 = - 3$ .

$4 s + 8 = - 3$

Step 6.2

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

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Step 6.2.1

Subtract $8$ from both sides of the equation.

$4 s = - 3 - 8$

Step 6.2.2

Subtract $8$ from $- 3$ .

$4 s = - 11$

Step 6.3

Divide each term in $4 s = - 11$ by $4$ and simplify.

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Step 6.3.1

Divide each term in $4 s = - 11$ by $4$ .

$\frac{4 s}{4} = \frac{- 11}{4}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $4$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{4 s}{4} = \frac{- 11}{4}$

Step 6.3.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 11}{4}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Move the negative in front of the fraction.

$s = - \frac{11}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{11}{4}$

Decimal Form:

$s = - 2.75$

Mixed Number Form:

$s = - 2 \frac{3}{4}$