Solve for b |7+5b|=3

$| 7 + 5 b | = 3$

Step 1

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

$7 + 5 b = \pm 3$

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.

$7 + 5 b = 3$

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

Subtract $7$ from both sides of the equation.

$5 b = 3 - 7$

Subtract $7$ from $3$ .

$5 b = - 4$

Divide each term in $5 b = - 4$ by $5$ and simplify.

Divide each term in $5 b = - 4$ by $5$ .

$\frac{5 b}{5} = \frac{- 4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 b}{5} = \frac{- 4}{5}$

Divide $b$ by $1$ .

$b = \frac{- 4}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{4}{5}$

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

$7 + 5 b = - 3$

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

Subtract $7$ from both sides of the equation.

$5 b = - 3 - 7$

Subtract $7$ from $- 3$ .

$5 b = - 10$

Divide each term in $5 b = - 10$ by $5$ and simplify.

Divide each term in $5 b = - 10$ by $5$ .

$\frac{5 b}{5} = \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 b}{5} = \frac{- 10}{5}$

Divide $b$ by $1$ .

$b = \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$b = - 2$

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

$b = - \frac{4}{5}, - 2$

Step 3

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{4}{5}, - 2$

Decimal Form:

$b = - 0.8, - 2$

Solve for b |7+5b|=3

Related Questions

Support LCMGCF.com by disabling your adblocker.