Algebra Examples

$- \frac{17}{4} s + 8 = \frac{3}{2} (\frac{1}{2} s + 6)$

Step 1

Simplify each term.

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Step 1.1

Combine $s$ and $\frac{17}{4}$ .

$- \frac{s \cdot 17}{4} + 8 = \frac{3}{2} \cdot (\frac{1}{2} s + 6)$

Step 1.2

Move $17$ to the left of $s$ .

$- \frac{17 s}{4} + 8 = \frac{3}{2} \cdot (\frac{1}{2} s + 6)$

Step 2

Simplify $\frac{3}{2} \cdot (\frac{1}{2} s + 6)$ .

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Step 2.1

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

$- \frac{17 s}{4} + 8 = \frac{3}{2} \cdot (\frac{s}{2} + 6)$

Step 2.2

Apply the distributive property.

$- \frac{17 s}{4} + 8 = \frac{3}{2} \cdot \frac{s}{2} + \frac{3}{2} \cdot 6$

Step 2.3

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

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Step 2.3.1

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

$- \frac{17 s}{4} + 8 = \frac{3 s}{2 \cdot 2} + \frac{3}{2} \cdot 6$

Step 2.3.2

Multiply $2$ by $2$ .

$- \frac{17 s}{4} + 8 = \frac{3 s}{4} + \frac{3}{2} \cdot 6$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $6$ .

$- \frac{17 s}{4} + 8 = \frac{3 s}{4} + \frac{3}{2} \cdot (2 (3))$

Step 2.4.2

Cancel the common factor.

$- \frac{17 s}{4} + 8 = \frac{3 s}{4} + \frac{3}{2} \cdot (2 \cdot 3)$

Step 2.4.3

Rewrite the expression.

$- \frac{17 s}{4} + 8 = \frac{3 s}{4} + 3 \cdot 3$

Step 2.5

Multiply $3$ by $3$ .

$- \frac{17 s}{4} + 8 = \frac{3 s}{4} + 9$

Step 3

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

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Step 3.1

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

$- \frac{17 s}{4} + 8 - \frac{3 s}{4} = 9$

Step 3.2

Combine the numerators over the common denominator.

$8 + \frac{- 17 s - 3 s}{4} = 9$

Step 3.3

Subtract $3 s$ from $- 17 s$ .

$8 + \frac{- 20 s}{4} = 9$

Step 3.4

Cancel the common factor of $- 20$ and $4$ .

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Step 3.4.1

Factor $4$ out of $- 20 s$ .

$8 + \frac{4 (- 5 s)}{4} = 9$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $4$ out of $4$ .

$8 + \frac{4 (- 5 s)}{4 (1)} = 9$

Step 3.4.2.2

Cancel the common factor.

$8 + \frac{4 (- 5 s)}{4 \cdot 1} = 9$

Step 3.4.2.3

Rewrite the expression.

$8 + \frac{- 5 s}{1} = 9$

Step 3.4.2.4

Divide $- 5 s$ by $1$ .

$8 - 5 s = 9$

Step 4

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

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Step 4.1

Subtract $8$ from both sides of the equation.

$- 5 s = 9 - 8$

Step 4.2

Subtract $8$ from $9$ .

$- 5 s = 1$

Step 5

Divide each term in $- 5 s = 1$ by $- 5$ and simplify.

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Step 5.1

Divide each term in $- 5 s = 1$ by $- 5$ .

$\frac{- 5 s}{- 5} = \frac{1}{- 5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 5 s}{- 5} = \frac{1}{- 5}$

Step 5.2.1.2

Divide $s$ by $1$ .

$s = \frac{1}{- 5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$s = - \frac{1}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{1}{5}$

Decimal Form:

$s = - 0.2$