Question

How do you solve for x in C = b – bx ?

Answer 1

Hint: To start with, we have the equation C = b – bx, from which we have to find the value of x. We can easily do that by distributive properties and changing sides of the equation. Only algebraic properties will be enough for solving our problem.

Complete step-by-step solution:
According to the problem, we are to solve the given equation C = b – bx to find the value of x.
To start with, we have, C = b – bx.
Now, we can separate the constants from the variable with algebraic operations. In this case we will still end up with an expression in C and b, as they are not given values.
As, C = b – bx,
Using the distributive property,
$\Rightarrow C=b\left( \text{1}- x \right)$
Now, dividing both sides by b, we get,
$\Rightarrow \dfrac{C}{b}=1-x$
Now, if we subtract 1 from both sides, we get,
$\Rightarrow \dfrac{C}{b}-1=-x$
Again, multiplying both sides by -1, we are getting,
$\Rightarrow x=1-\dfrac{C}{b}$
So, from this we can see, using the algebraic properties, we are getting the value of x.

Note: In this problem, we have found the value of x using simple algebraic properties. Now, the equation is given like in the form of an equation of a line, so, by getting the value C and b, x can be calculated. And if we compare the equations, C is implying the y coordinate of the line.