Question

Which procedure justifies whether Negative 3 x (5 minus 4) + 3 (x minus 6) is equivalent to Negative 12 x minus 6? The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30. The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (3) minus 6 = negative 42. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (negative 2) minus 6 = 18. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.

Answer 1

The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30

Or

Answer A

Explanation:

Apparently, we're trying to see if ...

-3(x)(5 -4) + 3(x -6) = -12(x) -6

by evaluating the expressions for x=2:

-3(2)(5-4) +3(2 -6) ?= -12(2) -6

-6 -12 ?= -24 -6

-18 ≠ -30 . . . . . . . . . shows expressions are not equivalent

Answer 2

The correct option is;

The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18

Explanation:

The parameters given are;

First expression 3 × X × (5 - 4) + 3 ×(X - 6)

Second expression -12 × X - 6

Therefore;

For the first expression, for all X, e have;

3 × X × 1 + 3 ×(X - 6) = -3·X + 3·X -18 = -18

The second expression gives -12·X - 6

When both expressions are equal, we have;

-12·X - 6 = -18

∴ X = (-18 + 6)/(-12) = 1

Hence the correct option is that the expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.