Answer:
Student B is correct
Student A failed to distribute -4 and -6 when opening the brackets in the first step
Step-by-step explanation:
The solution Student A gave was:
2x - 4(3x + 6) = -6(2x + 1) - 4
2x - 12x + 6 = -12x + 1 - 4
-10x + 6 = -12x - 3
2x = -9
x = -4 _1 2 ( -4 1/2)
The solution Student B gave was:
2x - 4(3x + 6) = -6(2x + 1) - 4
2x - 12x - 24 = -12x - 6 - 4
-10x - 24 = -12x - 10
2x = 14
x = 7
Student B is correct.
Explanation of the error:
Student A failed to distribute -4 and -6 when opening the brackets in the first step.
That is,
2x - 4(3x + 6) = -6(2x + 1) - 4
To open this bracket, we will distribute, -4 and -6 so that we get
2x (-4 × 3x) + (-4 × +6) = (-6×2x) + (-6 × +1) - 4
Then we will get
2x -12x -24 = -12x -6 -4
Adding the like terms
-10x - 24 = -12x - 10
Collecting like terms
-10x + 12x = -10 + 24
∴ 2x = 14
x = 14 / 2
Hence,
x = 7
A.
The contrapositive is formed by switching the hypothesis and conclusion of the statement and negating both of them.
You’d have to buy 3 shirts, with the 20% off the shirts would come out to $14.39. So $14.39 x 3 = $43.17. Now with the $10 off a $40 purchase your total cost would be $33.17.
ST is a midsegment, which tells you that BD=2(ST) or ST=½BD. Use that to substitute the values and find ST.
BD=2(ST)
29+x=2(2x+31)
29+x=4x+62
29=3x+62
-33=3x
x=-11
Now that we know x, we can substitute that into 2x+31 to find ST
ST=2x+31
ST=2(-11)+31
ST=-22+31
ST=9
