Algebra Examples

$9 (- \frac{2}{3} r + \frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1

Simplify $9 (- \frac{2}{3} r + \frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

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

$9 (- \frac{r \cdot 2}{3} + \frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.1.2

Move $2$ to the left of $r$ .

$9 (- \frac{2 r}{3} + \frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.2

Apply the distributive property.

$9 (- \frac{2 r}{3}) + 9 (\frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

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

$9 \frac{- 2 r}{3} + 9 (\frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.3.2

Factor $3$ out of $9$ .

$3 (3) \frac{- 2 r}{3} + 9 (\frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.3.3

Cancel the common factor.

$3 \cdot 3 \frac{- 2 r}{3} + 9 (\frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.3.4

Rewrite the expression.

$3 (- 2 r) + 9 (\frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.4

Multiply $- 2$ by $3$ .

$- 6 r + 9 (\frac{1}{3}) - 8 (\frac{3}{4} - \frac{1}{2} r) = 6 r$

Step 1.1.5

Cancel the common factor of $3$ .

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Step 1.1.5.1

Factor $3$ out of $9$ .

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

Step 1.1.5.2

Cancel the common factor.

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

Step 1.1.5.3

Rewrite the expression.

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

Step 1.1.6

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

$- 6 r + 3 - 8 (\frac{3}{4} - \frac{r}{2}) = 6 r$

Step 1.1.7

Apply the distributive property.

$- 6 r + 3 - 8 (\frac{3}{4}) - 8 (- \frac{r}{2}) = 6 r$

Step 1.1.8

Cancel the common factor of $4$ .

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Step 1.1.8.1

Factor $4$ out of $- 8$ .

$- 6 r + 3 + 4 (- 2) \frac{3}{4} - 8 (- \frac{r}{2}) = 6 r$

Step 1.1.8.2

Cancel the common factor.

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

Step 1.1.8.3

Rewrite the expression.

$- 6 r + 3 - 2 \cdot 3 - 8 (- \frac{r}{2}) = 6 r$

Step 1.1.9

Multiply $- 2$ by $3$ .

$- 6 r + 3 - 6 - 8 (- \frac{r}{2}) = 6 r$

Step 1.1.10

Cancel the common factor of $2$ .

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Step 1.1.10.1

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

$- 6 r + 3 - 6 - 8 \frac{- r}{2} = 6 r$

Step 1.1.10.2

Factor $2$ out of $- 8$ .

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

Step 1.1.10.3

Cancel the common factor.

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

Step 1.1.10.4

Rewrite the expression.

$- 6 r + 3 - 6 - 4 (- r) = 6 r$

Step 1.1.11

Multiply $- 1$ by $- 4$ .

$- 6 r + 3 - 6 + 4 r = 6 r$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $- 6 r$ and $4 r$ .

$- 2 r + 3 - 6 = 6 r$

Step 1.2.2

Subtract $6$ from $3$ .

$- 2 r - 3 = 6 r$

Step 2

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

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Step 2.1

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

$- 2 r - 3 - 6 r = 0$

Step 2.2

Subtract $6 r$ from $- 2 r$ .

$- 8 r - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$- 8 r = 3$

Step 4

Divide each term in $- 8 r = 3$ by $- 8$ and simplify.

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Step 4.1

Divide each term in $- 8 r = 3$ by $- 8$ .

$\frac{- 8 r}{- 8} = \frac{3}{- 8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 8 r}{- 8} = \frac{3}{- 8}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{3}{- 8}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$r = - \frac{3}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{3}{8}$

Decimal Form:

$r = - 0.375$