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: ax – c = bx + d ax – bx = d + c x (a – b) = d + c x = x equals StartFraction d plus c Over a minus b EndFraction. How can Victoria justify Step 3 of her work?

Answer 1

Answer:

Rewrite the expression on the left using the distributive property.

Step-by-step explanation:

Answer 2

Victoria can justify Step 3 of her work as follows.  

• The three steps of Victoria's work can be written as follows.

        $ax - bx = d + c$

        $x (a - b) = d + c$

        $x = \frac{d + c}{a-b}$

• As evident from the equations, in the second step, the product of x and (a-b) is equal to (d+c).
• Hence, the equation can be rearranged by cross multiplying the terms. The factor (a-b) must be brought to the denominator on the other side of the equation. In this way, x is isolated.