Solve for b |1+4b|=1

$| 1 + 4 b | = 1$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$1 + 4 b = \pm 1$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$1 + 4 b = 1$

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

Subtract $1$ from both sides of the equation.

$4 b = 1 - 1$

Subtract $1$ from $1$ .

$4 b = 0$

Divide each term in $4 b = 0$ by $4$ and simplify.

Divide each term in $4 b = 0$ by $4$ .

$\frac{4 b}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 b}{4} = \frac{0}{4}$

Divide $b$ by $1$ .

$b = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$b = 0$

Next, use the negative value of the $\pm$ to find the second solution.

$1 + 4 b = - 1$

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

Subtract $1$ from both sides of the equation.

$4 b = - 1 - 1$

Subtract $1$ from $- 1$ .

$4 b = - 2$

Divide each term in $4 b = - 2$ by $4$ and simplify.

Divide each term in $4 b = - 2$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$b = \frac{2 \cdot - 1}{2 \cdot 2}$

Cancel the common factor.

$b = \frac{2 \cdot - 1}{2 \cdot 2}$

Rewrite the expression.

$b = \frac{- 1}{2}$

Move the negative in front of the fraction.

$b = - \frac{1}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$b = 0, - \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$b = 0, - \frac{1}{2}$

Decimal Form:

$b = 0, - 0.5$

Solve for b |1+4b|=1

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