Which expressions would complete this equation so that it has one solution? 4(2x – 3) – 4x = choose exactly two answers that are correct.
a. 4x – 12
b. 3x – 4
c. 3(2x – 6)
d. 4(x – 5

First simplify 4(2x-3)-4x. Use distributive property: 4(2x)-4(3)-4x = 8x-12-4x = 4x-12. Now observe the answers. You can first eliminate a because you'll get the equation 4x-12=4x-12, which means x can be anything giving you an infinite amount of solutions. d is also not an option. Using distributive property, we find 4(x-5) = 4x-4(5) = 4x-20. The equation we get is 4x-12 = 4x-20, (or after subtracting 4x from each side, -12 = -20, which is not true), and this has no solution. There for, only b and c would work. (An easy way to do this problem is to find solutions that do not have 4 as the slope so that you only choose lines that are not parallel to 4x-12 [that means they don't intercept and have no solution] or the line that is on 4x-12 [meaning they're the same line and have infinite solutions].)

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