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Question
Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36
Given ⇒ 3(x − 4) + 5x = 9x − 36
Step 1 ⇒ 3x − 12 + 5x = 9x − 36
Step 2 ⇒ 3x + 5x − 12 = 9x − 36
Step 3 ⇒ 8x − 12 = 9x − 36
Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36
Step 5 ⇒ 0 − 12 = x − 36
Step 6 ⇒ −12 = x − 36
Step 7 ⇒ −12 + 36 = x − 36 + 36
Step 8 ⇒ 24 = x + 0
Step 9 ⇒ 24 = x
Which property yields Step 4?
Responses
A Subtraction Property of EqualitySubtraction Property of Equality
B Commutative Property of AdditionCommutative Property of Addition
C Addition Property of EqualityAddition Property of Equality
D Additive Inverse Property
D Additive Inverse Property
are you sure??
I apologize for the confusion. You are correct. The property that yields Step 4 is the Subtraction Property of Equality.
Given that x + y = 180, p + q = 180, and p = x. Show that y = q.
Which step would be used to prove the argument?
Responses
A x + p = 180x + p = 180
B x + y = p + qx + y = p + q
C y + q = 180y + q = 180
D 2x + 2y = 180
The correct step to prove the argument would be:
C y + q = 180
are you sure??
I apologize for the incorrect response. The correct step to prove the argument would be:
B x + y = p + q
Step 1: 4x + 5 < 6x + 1 (Given)
Step 2: −2x + 5 < 1 (Subtraction)
Step 3: −2x < 6 (Addition)
Step 4: x > −3 (Division)
Mia is trying to find her mistake in the problem shown. In which step did she first make a mistake?
Responses
A Step 1Step 1
B Step 2Step 2
C Step 3Step 3
D Step 4