Solve for b -4/7b+1/4=1/3b+1/2

$- \frac{4}{7} b + \frac{1}{4} = \frac{1}{3} b + \frac{1}{2}$

Step 1

Simplify each term.

Combine $b$ and $\frac{4}{7}$ .

$- \frac{b \cdot 4}{7} + \frac{1}{4} = \frac{1}{3} b + \frac{1}{2}$

Move $4$ to the left of $b$ .

$- \frac{4 b}{7} + \frac{1}{4} = \frac{1}{3} b + \frac{1}{2}$

Step 2

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

$- \frac{4 b}{7} + \frac{1}{4} = \frac{b}{3} + \frac{1}{2}$

Step 3

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

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

$- \frac{4 b}{7} + \frac{1}{4} - \frac{b}{3} = \frac{1}{2}$

To write $- \frac{4 b}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4 b}{7} \cdot \frac{3}{3} - \frac{b}{3} + \frac{1}{4} = \frac{1}{2}$

To write $- \frac{b}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{4 b}{7} \cdot \frac{3}{3} - \frac{b}{3} \cdot \frac{7}{7} + \frac{1}{4} = \frac{1}{2}$

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 b}{7}$ by $\frac{3}{3}$ .

$- \frac{4 b \cdot 3}{7 \cdot 3} - \frac{b}{3} \cdot \frac{7}{7} + \frac{1}{4} = \frac{1}{2}$

Multiply $7$ by $3$ .

$- \frac{4 b \cdot 3}{21} - \frac{b}{3} \cdot \frac{7}{7} + \frac{1}{4} = \frac{1}{2}$

Multiply $\frac{b}{3}$ by $\frac{7}{7}$ .

$- \frac{4 b \cdot 3}{21} - \frac{b \cdot 7}{3 \cdot 7} + \frac{1}{4} = \frac{1}{2}$

Multiply $3$ by $7$ .

$- \frac{4 b \cdot 3}{21} - \frac{b \cdot 7}{21} + \frac{1}{4} = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{- 4 b \cdot 3 - b \cdot 7}{21} + \frac{1}{4} = \frac{1}{2}$

Simplify each term.

Simplify the numerator.

Factor $b$ out of $- 4 b \cdot 3 - b \cdot 7$ .

Factor $b$ out of $- 4 b \cdot 3$ .

$\frac{b (- 4 \cdot 3) - b \cdot 7}{21} + \frac{1}{4} = \frac{1}{2}$

Factor $b$ out of $- b \cdot 7$ .

$\frac{b (- 4 \cdot 3) + b (- 1 \cdot 7)}{21} + \frac{1}{4} = \frac{1}{2}$

Factor $b$ out of $b (- 4 \cdot 3) + b (- 1 \cdot 7)$ .

$\frac{b (- 4 \cdot 3 - 1 \cdot 7)}{21} + \frac{1}{4} = \frac{1}{2}$

Multiply $- 4$ by $3$ .

$\frac{b (- 12 - 1 \cdot 7)}{21} + \frac{1}{4} = \frac{1}{2}$

Multiply $- 1$ by $7$ .

$\frac{b (- 12 - 7)}{21} + \frac{1}{4} = \frac{1}{2}$

Subtract $7$ from $- 12$ .

$\frac{b \cdot - 19}{21} + \frac{1}{4} = \frac{1}{2}$

Move $- 19$ to the left of $b$ .

$\frac{- 19 \cdot b}{21} + \frac{1}{4} = \frac{1}{2}$

Move the negative in front of the fraction.

$- \frac{19 b}{21} + \frac{1}{4} = \frac{1}{2}$

Step 4

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

Subtract $\frac{1}{4}$ from both sides of the equation.

$- \frac{19 b}{21} = \frac{1}{2} - \frac{1}{4}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{19 b}{21} = \frac{1}{2} \cdot \frac{2}{2} - \frac{1}{4}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{19 b}{21} = \frac{2}{2 \cdot 2} - \frac{1}{4}$

Multiply $2$ by $2$ .

$- \frac{19 b}{21} = \frac{2}{4} - \frac{1}{4}$

Combine the numerators over the common denominator.

$- \frac{19 b}{21} = \frac{2 - 1}{4}$

Subtract $1$ from $2$ .

$- \frac{19 b}{21} = \frac{1}{4}$

Step 5

Multiply both sides of the equation by $- \frac{21}{19}$ .

$- \frac{21}{19} (- \frac{19 b}{21}) = - \frac{21}{19} \cdot \frac{1}{4}$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{21}{19} (- \frac{19 b}{21})$ .

Cancel the common factor of $21$ .

Move the leading negative in $- \frac{21}{19}$ into the numerator.

$\frac{- 21}{19} (- \frac{19 b}{21}) = - \frac{21}{19} \cdot \frac{1}{4}$

Move the leading negative in $- \frac{19 b}{21}$ into the numerator.

$\frac{- 21}{19} \cdot \frac{- 19 b}{21} = - \frac{21}{19} \cdot \frac{1}{4}$

Factor $21$ out of $- 21$ .

$\frac{21 (- 1)}{19} \cdot \frac{- 19 b}{21} = - \frac{21}{19} \cdot \frac{1}{4}$

Cancel the common factor.

$\frac{21 \cdot - 1}{19} \cdot \frac{- 19 b}{21} = - \frac{21}{19} \cdot \frac{1}{4}$

Rewrite the expression.

$\frac{- 1}{19} (- 19 b) = - \frac{21}{19} \cdot \frac{1}{4}$

Cancel the common factor of $19$ .

Factor $19$ out of $- 19 b$ .

$\frac{- 1}{19} (19 (- b)) = - \frac{21}{19} \cdot \frac{1}{4}$

Cancel the common factor.

$\frac{- 1}{19} (19 (- b)) = - \frac{21}{19} \cdot \frac{1}{4}$

Rewrite the expression.

$- - b = - \frac{21}{19} \cdot \frac{1}{4}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - \frac{21}{19} \cdot \frac{1}{4}$

Multiply $b$ by $1$ .

$b = - \frac{21}{19} \cdot \frac{1}{4}$

Simplify the right side.

Multiply $- \frac{21}{19} \cdot \frac{1}{4}$ .

Multiply $\frac{1}{4}$ by $\frac{21}{19}$ .

$b = - \frac{21}{4 \cdot 19}$

Multiply $4$ by $19$ .

$b = - \frac{21}{76}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{21}{76}$

Decimal Form:

$b = - 0.27631578 \dots$

Solve for b -4/7b+1/4=1/3b+1/2

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