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?

Rewrite the expression on the left using the distributive property.
Multiply both sides by x.
Rewrite the expression on the left using subtraction.
Divide both sides by x.

1 answer

Victoria can justify Step 3 of her work by rewriting the left side of the equation using the distributive property. By doing this, she combines the x terms and factors out x. This transforms the equation into x(a - b) = d + c, from which she can then divide both sides by (a - b) to isolate x.