Algebra Examples

$\frac{2}{5} (5 + 10 s) = - \frac{3}{2} (\frac{2}{3} s - 4) + 3$

Step 1

Simplify $\frac{2}{5} \cdot (5 + 10 s)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{5} \cdot (5 + 10 s) = - \frac{3}{2} \cdot (\frac{2}{3} s - 4) + 3$

Step 1.2

Simplify by adding zeros.

$\frac{2}{5} \cdot (5 + 10 s) = - \frac{3}{2} \cdot (\frac{2}{3} s - 4) + 3$

Step 1.3

Apply the distributive property.

$\frac{2}{5} \cdot 5 + \frac{2}{5} (10 s) = - \frac{3}{2} \cdot (\frac{2}{3} s - 4) + 3$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Cancel the common factor.

$\frac{2}{5} \cdot 5 + \frac{2}{5} (10 s) = - \frac{3}{2} \cdot (\frac{2}{3} s - 4) + 3$

Step 1.4.2

Rewrite the expression.

$2 + \frac{2}{5} (10 s) = - \frac{3}{2} \cdot (\frac{2}{3} s - 4) + 3$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $10 s$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 1.6

Multiply $2$ by $2$ .

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

Step 2

Simplify $- \frac{3}{2} \cdot (\frac{2}{3} s - 4) + 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

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

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

Step 2.1.3.2

Factor $3$ out of $- 3$ .

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

Step 2.1.3.3

Cancel the common factor.

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

Step 2.1.3.4

Rewrite the expression.

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

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Factor $2$ out of $2 s$ .

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

Step 2.1.4.2

Cancel the common factor.

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

Step 2.1.4.3

Rewrite the expression.

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

Step 2.1.5

Cancel the common factor of $2$ .

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Step 2.1.5.1

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

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

Step 2.1.5.2

Factor $2$ out of $- 4$ .

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

Step 2.1.5.3

Cancel the common factor.

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

Step 2.1.5.4

Rewrite the expression.

$2 + 4 s = - 1 s - 3 \cdot - 2 + 3$

Step 2.1.6

Multiply $- 3$ by $- 2$ .

$2 + 4 s = - 1 s + 6 + 3$

Step 2.1.7

Rewrite $- 1 s$ as $- s$ .

$2 + 4 s = - s + 6 + 3$

Step 2.2

Add $6$ and $3$ .

$2 + 4 s = - s + 9$

Step 3

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

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Step 3.1

Add $s$ to both sides of the equation.

$2 + 4 s + s = 9$

Step 3.2

Add $4 s$ and $s$ .

$2 + 5 s = 9$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

$5 s = 9 - 2$

Step 4.2

Subtract $2$ from $9$ .

$5 s = 7$

Step 5

Divide each term in $5 s = 7$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 s = 7$ by $5$ .

$\frac{5 s}{5} = \frac{7}{5}$

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.

$\frac{5 s}{5} = \frac{7}{5}$

Step 5.2.1.2

Divide $s$ by $1$ .

$s = \frac{7}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$s = \frac{7}{5}$

Decimal Form:

$s = 1.4$

Mixed Number Form:

$s = 1 \frac{2}{5}$