Solve for b 6(1 1/4+b)=10

$6 (1 \frac{1}{4} + b) = 10$

Step 1

Simplify the left side.

Simplify $6 (1 \frac{1}{4} + b)$ .

Convert $1 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$6 (1 + \frac{1}{4} + b) = 10$

Add $1$ and $\frac{1}{4}$ .

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

$6 (\frac{4}{4} + \frac{1}{4} + b) = 10$

Combine the numerators over the common denominator.

$6 (\frac{4 + 1}{4} + b) = 10$

Add $4$ and $1$ .

$6 (\frac{5}{4} + b) = 10$

Apply the distributive property.

$6 (\frac{5}{4}) + 6 b = 10$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 (3) \frac{5}{4} + 6 b = 10$

Factor $2$ out of $4$ .

$2 \cdot 3 \frac{5}{2 \cdot 2} + 6 b = 10$

Cancel the common factor.

$2 \cdot 3 \frac{5}{2 \cdot 2} + 6 b = 10$

Rewrite the expression.

$3 (\frac{5}{2}) + 6 b = 10$

Combine $3$ and $\frac{5}{2}$ .

$\frac{3 \cdot 5}{2} + 6 b = 10$

Multiply $3$ by $5$ .

$\frac{15}{2} + 6 b = 10$

Step 2

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

Subtract $\frac{15}{2}$ from both sides of the equation.

$6 b = 10 - \frac{15}{2}$

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 b = 10 \cdot \frac{2}{2} - \frac{15}{2}$

Combine $10$ and $\frac{2}{2}$ .

$6 b = \frac{10 \cdot 2}{2} - \frac{15}{2}$

Combine the numerators over the common denominator.

$6 b = \frac{10 \cdot 2 - 15}{2}$

Simplify the numerator.

Multiply $10$ by $2$ .

$6 b = \frac{20 - 15}{2}$

Subtract $15$ from $20$ .

$6 b = \frac{5}{2}$

Step 3

Divide each term in $6 b = \frac{5}{2}$ by $6$ and simplify.

Divide each term in $6 b = \frac{5}{2}$ by $6$ .

$\frac{6 b}{6} = \frac{\frac{5}{2}}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 b}{6} = \frac{\frac{5}{2}}{6}$

Divide $b$ by $1$ .

$b = \frac{\frac{5}{2}}{6}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $\frac{5}{2} \cdot \frac{1}{6}$ .

Multiply $\frac{5}{2}$ by $\frac{1}{6}$ .

$b = \frac{5}{2 \cdot 6}$

Multiply $2$ by $6$ .

$b = \frac{5}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = \frac{5}{12}$

Decimal Form:

$b = 0.41\overline{6}$

Solve for b 6(1 1/4+b)=10

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