Question

b/2b-(6+6b)= -2/7 solve the equation

Answer 1

Let's solve your equation step-by-step.

$\frac{b}{2b}-(6+6b)=\frac{-2}{7}$

$\frac{b}{2b}+-6+-6b=\frac{-2}{7}$

Multiply all terms by b and cancel:

$\frac{b}{2}+ -6b+(-6b)(b)=\frac{-2b}{7}$

(Simplify both sides of the equation)

$-6b^{2}+\frac{-11}{2}b=\frac{-2}{7}b$

(Subtract $\frac{-2}{7}b$ from both sides)

$-6b^{2}+\frac{-11}{2}b-\frac{-2}{7}b =\frac{-2}{7}b-\frac{-2}{7}b$

$-6b^{2}+\frac{-73}{14}b=0$

(Factor left side of the equation)

$(-b)(-6b+\frac{73}{14} )=0$

(Set factors equal to 0)

$-b=0\ or \ 6b+\frac{73}{14}=0$

$b=0 \ or \ b=\frac{-73}{84}$

Check answers. (Plug them in to make sure they work.)

First, we'll try with $b=0$

⇒ $\frac{0}{2\times 0 } -(6+(6\times 0))$

⇒ $\frac{0}{0}-(6+(6)(0))$

⇒ $\frac{0}{0}-(6+0)$

⇒ $\frac{0}{0}-6$

⇒ $0$

∴ $b\neq 0$

Now, we'll try $b=\frac{-73}{84}$

$\frac{-\frac{73}{84}}{2\times -\frac{73}{84}}-(6+\left(6\times -\frac{73}{84})\right)$

$\frac{\frac{-73}{84} }{2\times \frac{-73}{84} } -(6+(6\times \frac{-73}{84}))$

$\frac{1}{2}-(6+(6(\frac{-73}{84})))$

$\frac{1}{2}-(6+\frac{-73}{14})$

$\frac{1}{2}-\frac{11}{14}$

$\frac{-2}{7}$

∴$b=\frac{-73}{84}$

∴$b=\frac{-73}{84}$ in the equation ⇒ $\frac{b}{2b}-(6+6b)=\frac{-2}{7}$