Precalculus Examples

$- 2 = \frac{7}{6} (4) + b$

Step 1

Rewrite the equation as $\frac{7}{6} \cdot 4 + b = - 2$ .

$\frac{7}{6} \cdot 4 + b = - 2$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $6$ .

$\frac{7}{2 (3)} \cdot 4 + b = - 2$

Step 2.1.2

Factor $2$ out of $4$ .

$\frac{7}{2 \cdot 3} \cdot (2 \cdot 2) + b = - 2$

Step 2.1.3

Cancel the common factor.

$\frac{7}{2 \cdot 3} \cdot (2 \cdot 2) + b = - 2$

Step 2.1.4

Rewrite the expression.

$\frac{7}{3} \cdot 2 + b = - 2$

Step 2.2

Combine $\frac{7}{3}$ and $2$ .

$\frac{7 \cdot 2}{3} + b = - 2$

Step 2.3

Multiply $7$ by $2$ .

$\frac{14}{3} + b = - 2$

Step 3

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

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Step 3.1

Subtract $\frac{14}{3}$ from both sides of the equation.

$b = - 2 - \frac{14}{3}$

Step 3.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - 2 \cdot \frac{3}{3} - \frac{14}{3}$

Step 3.3

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

$b = \frac{- 2 \cdot 3}{3} - \frac{14}{3}$

Step 3.4

Combine the numerators over the common denominator.

$b = \frac{- 2 \cdot 3 - 14}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 2$ by $3$ .

$b = \frac{- 6 - 14}{3}$

Step 3.5.2

Subtract $14$ from $- 6$ .

$b = \frac{- 20}{3}$

Step 3.6

Move the negative in front of the fraction.

$b = - \frac{20}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{20}{3}$

Decimal Form:

$b = - 6.\overline{6}$

Mixed Number Form:

$b = - 6 \frac{2}{3}$