Question

Jalil and Victoria are each asked to solve the equation ax – c = bx + d for x. Jalil says it is not possible to isolate x because each x has a different unknown coefficient. Victoria believes there is a solution, and shows Jalil her work:

Answer 1

`x=(d+c)/(a-b)`

Explanation:

The equation is:

a x - c = b x + d

so we subtract b x from both sides to group the terms that contain x on the left:

a x - b x - c = d

add c to both sides to isolate the terms in x on the left:

a x - b x = d + c

extract "x" as common factor on the left using distributive property backwards:

x (a - b) = d + c

divide both sides by the quantity (a - b) to isolate the "x":

x = (d + c) / (a - b)

or:
`x=(d+c)/(a-b)`