Question

If x + 6 = 11, which statement is false?

A) The equation x + 11 = 6 is equivalent to x + 6 = 11 since 6 + 11 = 11 + 6.
B) The equation 2x + 12 = 22 is equivalent to x + 6 = 11 since 2(x + 6) = 2(11).
C) The equation x + 9 = 14 is equivalent to x + 6 = 11 since (x + 6) + 3 = 11 + 3.
D) The equation x − 1 = 4 is equivalent to x + 6 = 11 since (x + 6) − 7 = 11 − 7.

Answer 1

A is correct. explanation above

Answer 2

A) The equation x + 11 = 6 is equivalent to x + 6 = 11 since 6 + 11 = 11 + 6 is false.

Explanation:

A) One simple way to test the truth of this statement is to solve for x:

In x + 11 = 6, subtracting 11 from both sides leaves x = -5.

In x + 6 = 11, subtracting 6 from both sides leaves x = 5.

-5 does not equal 5, so the equations are not equivalent.

Therefore, A) is false.