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

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

Combine $\frac{1}{4}$ and $b$ .

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

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

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

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

Add $\frac{b}{2}$ to both sides of the equation.

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $b$ and $b \cdot 2$ .

Reorder $b$ and $2$ .

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

Add $b$ and $2 \cdot b$ .

$\frac{3 b}{4} + 1 = 3$

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

Subtract $1$ from both sides of the equation.

$\frac{3 b}{4} = 3 - 1$

Subtract $1$ from $3$ .

$\frac{3 b}{4} = 2$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 b}{4} = \frac{4}{3} \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 b}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 b}{4} = \frac{4}{3} \cdot 2$

Rewrite the expression.

$\frac{1}{3} (3 b) = \frac{4}{3} \cdot 2$

Cancel the common factor of $3$ .

Factor $3$ out of $3 b$ .

$\frac{1}{3} (3 (b)) = \frac{4}{3} \cdot 2$

Cancel the common factor.

$\frac{1}{3} (3 b) = \frac{4}{3} \cdot 2$

Rewrite the expression.

$b = \frac{4}{3} \cdot 2$

Simplify the right side.

Multiply $\frac{4}{3} \cdot 2$ .

Combine $\frac{4}{3}$ and $2$ .

$b = \frac{4 \cdot 2}{3}$

Multiply $4$ by $2$ .

$b = \frac{8}{3}$

The result can be shown in multiple forms.

Exact Form:

$b = \frac{8}{3}$

Decimal Form:

$b = 2.\overline{6}$

Mixed Number Form:

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

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

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