Question

Drag each expression to show whether it is equivalent to 54x + 18, 18(3x – 1), or (6 • 9x) + (6 • 1).  A.54x + 6 B(9 • 6x) – (9 • 2) C.54x – 18 18(3x + 1) D(6 • 9x) + (6 • 3) E.3(18x+2)

Answer 1

54x + 18 -> (6 • 9x) + (6 • 3) and 18(3x + 1)

18(3x – 1) -> (9 • 6x) – (9 • 2) and 54x – 18

(6 • 9x) + (6 • 1) -> 3(18x+2) and 54x + 6

Explanation:

Rewrite expressions, so that, we can compare them.

Distributing 18(3x – 1) gives

18(3x – 1) = 18*3x - 18*1 = 54x - 18

In 18(3x + 1) and 3(18x+2) we can perform similarly

18*(3x + 1) = 18*3x + 18*1 = 54x + 18

3*(18x+2) = 3*18x + 3*2 = 54x + 6

Multiplying each term inside parenthesis in (6*9x) + (6*1) gives

(6*9x) + (6*1) = 54x + 6

In (9*6x) – (9*2) and (6*9x) + (6*3) we can perform similarly

(9*6x) – (9*2) = 54x - 18

(6*9x) + (6*3) = 54x + 18