Solve for b (b-1)/5+1/6=5/2

$\frac{b - 1}{5} + \frac{1}{6} = \frac{5}{2}$

Step 1

Simplify $\frac{b - 1}{5} + \frac{1}{6}$ .

To write $\frac{b - 1}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{b - 1}{5} \cdot \frac{6}{6} + \frac{1}{6} = \frac{5}{2}$

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{b - 1}{5} \cdot \frac{6}{6} + \frac{1}{6} \cdot \frac{5}{5} = \frac{5}{2}$

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{b - 1}{5}$ by $\frac{6}{6}$ .

$\frac{(b - 1) \cdot 6}{5 \cdot 6} + \frac{1}{6} \cdot \frac{5}{5} = \frac{5}{2}$

Multiply $5$ by $6$ .

$\frac{(b - 1) \cdot 6}{30} + \frac{1}{6} \cdot \frac{5}{5} = \frac{5}{2}$

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{(b - 1) \cdot 6}{30} + \frac{5}{6 \cdot 5} = \frac{5}{2}$

Multiply $6$ by $5$ .

$\frac{(b - 1) \cdot 6}{30} + \frac{5}{30} = \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{(b - 1) \cdot 6 + 5}{30} = \frac{5}{2}$

Simplify the numerator.

Apply the distributive property.

$\frac{b \cdot 6 - 1 \cdot 6 + 5}{30} = \frac{5}{2}$

Move $6$ to the left of $b$ .

$\frac{6 \cdot b - 1 \cdot 6 + 5}{30} = \frac{5}{2}$

Multiply $- 1$ by $6$ .

$\frac{6 \cdot b - 6 + 5}{30} = \frac{5}{2}$

Add $- 6$ and $5$ .

$\frac{6 b - 1}{30} = \frac{5}{2}$

Step 2

Multiply both sides by $30$ .

$\frac{6 b - 1}{30} \cdot 30 = \frac{5}{2} \cdot 30$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{6 b - 1}{30} \cdot 30 = \frac{5}{2} \cdot 30$

Rewrite the expression.

$6 b - 1 = \frac{5}{2} \cdot 30$

Simplify the right side.

Simplify $\frac{5}{2} \cdot 30$ .

Cancel the common factor of $2$ .

Factor $2$ out of $30$ .

$6 b - 1 = \frac{5}{2} \cdot (2 (15))$

Cancel the common factor.

$6 b - 1 = \frac{5}{2} \cdot (2 \cdot 15)$

Rewrite the expression.

$6 b - 1 = 5 \cdot 15$

Multiply $5$ by $15$ .

$6 b - 1 = 75$

Step 4

Solve for $b$ .

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

Add $1$ to both sides of the equation.

$6 b = 75 + 1$

Add $75$ and $1$ .

$6 b = 76$

Divide each term in $6 b = 76$ by $6$ and simplify.

Divide each term in $6 b = 76$ by $6$ .

$\frac{6 b}{6} = \frac{76}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 b}{6} = \frac{76}{6}$

Divide $b$ by $1$ .

$b = \frac{76}{6}$

Simplify the right side.

Cancel the common factor of $76$ and $6$ .

Factor $2$ out of $76$ .

$b = \frac{2 (38)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$b = \frac{2 \cdot 38}{2 \cdot 3}$

Cancel the common factor.

$b = \frac{2 \cdot 38}{2 \cdot 3}$

Rewrite the expression.

$b = \frac{38}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \frac{38}{3}$

Decimal Form:

$b = 12.\overline{6}$

Mixed Number Form:

$b = 12 \frac{2}{3}$

Solve for b (b-1)/5+1/6=5/2

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