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Test used to see the strengths and weaknesses in equality using APE (Addition Property of Equality) and SPE (Subtraction Property of Equality).
Questions and Answers
1.
How will you solve for x in:
-3(x-1)+5(x+2)=x-2?
It must be included in your answer.
Solution
Property used
Explanation
Answer/Root
2.
What is SPE?
A.
If x=y, then x-y=z-y.
B.
If x=y, then x-z=y-z.
C.
If x=z, then x-y=y-x.
Correct Answer B. If x=y, then x-z=y-z.
Explanation The given answer is a valid statement based on the transitive property of equality. According to the transitive property, if two quantities are equal to a third quantity, then they are equal to each other. In this case, if x=y and x-z=y-z, it can be deduced that x-z=y-z. Thus, the answer is correct.
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3.
What is APE?
A.
If x=y, then x+y+z=z+z.
B.
If x=y, then x+z=y+x.
C.
If x=y, then x+z=y+z.
Correct Answer C. If x=y, then x+z=y+z.
Explanation The given answer states that if x is equal to y, then adding z to both x and y will result in the same value. This is a basic property of equality, where adding the same value to both sides of an equation does not change its truth. Therefore, if x is equal to y, then adding z to both sides will still result in equality, making x+z=y+z.
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4.
X-1=3. Solve for x.
A.
4
B.
2
C.
-2
Correct Answer A. 4
Explanation To solve the equation x-1=3, we need to isolate the variable x. To do this, we can add 1 to both sides of the equation. This will cancel out the -1 on the left side, leaving us with x=4. Therefore, the correct answer is 4.
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5.
3x-4=5. Solve for x.
A.
9
B.
-9
C.
3
Correct Answer C. 3
Explanation To solve the equation 3x-4=5, we need to isolate the variable x. First, we add 4 to both sides of the equation to get 3x=9. Then, we divide both sides by 3 to solve for x, which gives us x=3. Therefore, the correct answer is 3.
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6.
7x+3=17, then x=2, then 7(2)+3=17.
A.
True
B.
False
Correct Answer A. True
Explanation The given equation states that 7x + 3 = 17. To find the value of x, we need to isolate it on one side of the equation. By subtracting 3 from both sides, we get 7x = 14. Dividing both sides by 7, we find that x = 2. Substituting this value back into the original equation, we get 7(2) + 3 = 17, which is true. Therefore, the statement is true.
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7.
If 6x+3=21, then x=_______.
Correct Answer 3
Explanation The given equation is 6x+3=21. To solve for x, we need to isolate x on one side of the equation. Subtracting 3 from both sides, we get 6x = 18. Dividing both sides by 6, we find that x = 3.
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8.
What property is expressed in if 4x-2=3, then 2x=2x-1
Correct Answer SPE Subtraction Property Subtraction Subtraction Property of Equality
Explanation The property expressed in the given statement is the Subtraction Property of Equality. This property states that if we subtract the same quantity from both sides of an equation, the two sides remain equal. In this case, we are subtracting 2x from both sides of the equation 2x = 2x - 1, which is an application of the Subtraction Property of Equality. Therefore, the correct answer is Subtraction Property of Equality.
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9.
What property is expressed in if 4x-2=3, then 6x+2=2x+7
Correct Answer APE Addition Addition Property Addition Property of Equality
Explanation The property expressed in the given equation is the Addition Property of Equality. This property states that if the same number is added to both sides of an equation, the equality is still maintained. In this case, by adding 2 to both sides of the equation 6x+2=2x+7, we are applying the Addition Property of Equality to maintain the equality of the equation. The other terms mentioned, APE and Addition, are simply alternative ways of referring to the Addition Property of Equality.
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10.
3x-3=2 then 5x-2=2x+3. What property is Illustrated? _________ Property of Equality
Correct Answer Addition
Explanation The property illustrated in this equation is the Addition Property of Equality. This property states that if you add the same number to both sides of an equation, the equality is still maintained. In the given equation, 3x - 3 = 2, the number 3 is added to both sides to isolate the variable. Similarly, in the equation 5x - 2 = 2x + 3, the number 2 is added to both sides to isolate the variable. Therefore, the Addition Property of Equality is being used in this scenario.