Algebra Examples

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

Step 1

Simplify $\frac{2}{3} \cdot (\frac{1}{2} s + 6) - 4 (\frac{3}{2} - \frac{3}{2} s)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Cancel the common factor.

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

Step 1.1.3.2

Rewrite the expression.

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

Step 1.1.4

Combine $\frac{1}{3}$ and $s$ .

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

Step 1.1.5

Cancel the common factor of $3$ .

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Step 1.1.5.1

Factor $3$ out of $6$ .

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

Step 1.1.5.2

Cancel the common factor.

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

Step 1.1.5.3

Rewrite the expression.

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

Step 1.1.6

Multiply $2$ by $2$ .

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

Step 1.1.7

Simplify each term.

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Step 1.1.7.1

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

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

Step 1.1.7.2

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

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

Step 1.1.8

Apply the distributive property.

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

Step 1.1.9

Cancel the common factor of $2$ .

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Step 1.1.9.1

Factor $2$ out of $- 4$ .

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

Step 1.1.9.2

Cancel the common factor.

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

Step 1.1.9.3

Rewrite the expression.

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

Step 1.1.10

Multiply $- 2$ by $3$ .

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

Step 1.1.11

Cancel the common factor of $2$ .

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Step 1.1.11.1

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

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

Step 1.1.11.2

Factor $2$ out of $- 4$ .

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

Step 1.1.11.3

Cancel the common factor.

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

Step 1.1.11.4

Rewrite the expression.

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

Step 1.1.12

Multiply $- 3$ by $- 2$ .

$\frac{s}{3} + 4 - 6 + 6 s = 6 s$

Step 1.2

To write $6 s$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

Combine $6 s$ and $\frac{3}{3}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Find the common denominator.

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Step 1.5.1

Write $4$ as a fraction with denominator $1$ .

$\frac{s + 6 s \cdot 3}{3} + \frac{4}{1} - 6 = 6 s$

Step 1.5.2

Multiply $\frac{4}{1}$ by $\frac{3}{3}$ .

$\frac{s + 6 s \cdot 3}{3} + \frac{4}{1} \cdot \frac{3}{3} - 6 = 6 s$

Step 1.5.3

Multiply $\frac{4}{1}$ by $\frac{3}{3}$ .

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

Step 1.5.4

Write $- 6$ as a fraction with denominator $1$ .

$\frac{s + 6 s \cdot 3}{3} + \frac{4 \cdot 3}{3} + \frac{- 6}{1} = 6 s$

Step 1.5.5

Multiply $\frac{- 6}{1}$ by $\frac{3}{3}$ .

$\frac{s + 6 s \cdot 3}{3} + \frac{4 \cdot 3}{3} + \frac{- 6}{1} \cdot \frac{3}{3} = 6 s$

Step 1.5.6

Multiply $\frac{- 6}{1}$ by $\frac{3}{3}$ .

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

Step 1.6

Combine the numerators over the common denominator.

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

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $3$ by $6$ .

$\frac{s + 18 s + 4 \cdot 3 - 6 \cdot 3}{3} = 6 s$

Step 1.7.2

Multiply $4$ by $3$ .

$\frac{s + 18 s + 12 - 6 \cdot 3}{3} = 6 s$

Step 1.7.3

Multiply $- 6$ by $3$ .

$\frac{s + 18 s + 12 - 18}{3} = 6 s$

Step 1.8

Simplify by adding terms.

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Step 1.8.1

Add $s$ and $18 s$ .

$\frac{19 s + 12 - 18}{3} = 6 s$

Step 1.8.2

Subtract $18$ from $12$ .

$\frac{19 s - 6}{3} = 6 s$

Step 2

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

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Step 2.1

Subtract $6 s$ from both sides of the equation.

$\frac{19 s - 6}{3} - 6 s = 0$

Step 2.2

To write $- 6 s$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{19 s - 6}{3} - 6 s \cdot \frac{3}{3} = 0$

Step 2.3

Combine $- 6 s$ and $\frac{3}{3}$ .

$\frac{19 s - 6}{3} + \frac{- 6 s \cdot 3}{3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{19 s - 6 - 6 s \cdot 3}{3} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $- 6$ .

$\frac{19 s - 6 - 18 s}{3} = 0$

Step 2.5.2

Subtract $18 s$ from $19 s$ .

$\frac{s - 6}{3} = 0$

Step 3

Set the numerator equal to zero.

$s - 6 = 0$

Step 4

Add $6$ to both sides of the equation.

$s = 6$