Question

How do solve $\dfrac{13-b}{6}=\dfrac{2-.5b}{4}$ ?

Answer 1

Hint: At first, we multiply both sides of the equation by $6$ and then by $4$ . Doing so removes the fractions. After that, we perform some basic arithmetic operations to simplify the expression and finally, we get a solution for $b$ , which is the final solution to our equation.

Complete step by step solution:
The given equation that we have at our disposal is,
$\dfrac{13-b}{6}=\dfrac{2-.5b}{4}$
Let us first multiply both sides of the above equation first with $6$ . The equation thus becomes,
$\Rightarrow \dfrac{13-b}{6}\times 6=\dfrac{2-.5b}{4}\times 6$
This upon simplification gives,
$\Rightarrow 13-b=\dfrac{2-.5b}{4}\times 6$
Let us now multiply both sides of the above equation by $4$ . The equation thus becomes,
$\Rightarrow \left( 13-b \right)\times 4=\dfrac{2-.5b}{4}\times 6\times 4$
This upon simplification gives,
$\Rightarrow \left( 13-b \right)\times 4=\left( 2-.5b \right)\times 6$
Let us now apply the distributive property in the above equation. The equation thus becomes,
$\Rightarrow 26-4b=12-3b$
Let us now subtract $12$ from both sides of the above equation. The equation thus becomes,
$\Rightarrow 26-4b-12=12-3b-12$
This upon simplification gives,
$\Rightarrow 14-4b=-3b$
Adding $4b$ to both the sides of the above equation, we get,
$\Rightarrow 14-4b+4b=-3b+4b$
This upon simplification gives,
$\Rightarrow 14=b$
The above equation can be rewritten as,
$\Rightarrow b=14$
Therefore, we can conclude that the solution to the given equation is $b=14$ .

Note:
In these types of problems, it is always better to remove the fractions somehow at first. Fractions create mistakes, so better to avoid them. Also, we should try our best not to develop any fraction in between our solutions. We should always make the expressions to their simplest form for an easier solution. We can also solve the problem by bringing the entire right hand side term to the left hand side and then, using the LCM of denominators, we can solve for the fractions.