Could someone please show me what I did worng in my math questions? any help will be greatly appreciated! I put my teachers response under the questions
4. Solve:
5|2x + 1 | = 55
Divide both side by 5: |2x+1|=11
2x+1=11 and 2x+1= -1
+1 +1 +1 +1
2x = 12 2x = -10
X=5 x=-6
What my teacher said was wrong~~
2x+1=11 and 2x+1= -11 YES, for both of these!
+1 +1 Absolutely not, why?
5. Solve:
1/2|4x – 8| - 7 = 3
½|4x-8|=10
|4x-8|=20
4x-8=20 or -4x+8=20
X=7 or x=-3
What my teacher said was wrong~~ missing steps at the end....
6. Evaluate the given expressions when a = 3, b = -3, c = 4, and d = -1.
c|a-b| + d
= -3|3-(-3)|
=-1(-6)=-6
Answer is -6
What my teacher said was wrong~~ incorrect substitution at the end
For #4, you are subtracting 1 from each part and not adding it.
subtracting 1 gives you 2x = 10 and
2x = -12
You had the right idea, but the adding 1 is wrong, you really subtracted 1.
Teacher was probably looking for you to show the adding 8 and dividing by 4 and for the other one subtracting 8 and dividing by -4.
4|3-(-3| + -1
4(6) + -1
24 +-1 = 23 It looks like you substituted -3 for c instead of 4
In question 4, you correctly divided both sides of the equation by 5 to get |2x+1|=11. However, instead of writing 2x+1=11 and 2x+1= -11, you wrote 2x+1=11 and 2x+1= -1. This is where you made a mistake. The correct equations should be 2x+1=11 and 2x+1= -11.
Your teacher pointed out that when you added 1 to both sides of the equation, you made an error. Adding 1 to both sides should have been done to eliminate the 1 on the right side of the equation, not to adjust the constant term on both sides. Therefore, the step should have been skipped.
In question 5, you correctly started by subtracting 7 from both sides of the equation to get 1/2|4x-8|=10. Then you multiplied both sides by 2 to get |4x-8|=20, which is correct. However, your teacher mentioned that you missed some steps at the end. The missing steps are solving the absolute value equation separately for both cases.
For the first case, 4x-8=20, you correctly added 8 to both sides and divided by 4 to solve for x, which gives x=7.
For the second case, -4x+8=20, you correctly added 8 to both sides and divided by -4 to solve for x, which gives x=-3.
So the correct solutions are x=7 or x=-3.
In question 6, you substituted the given values correctly into the expression c|a-b| + d as c|3-(-3)| + (-1). However, your teacher mentioned that you made an incorrect substitution at the end. Based on the given values, c=4, a=3, b=-3, and d=-1. Therefore, the correct evaluation of the expression is 4|3-(-3)| + (-1) = 4|6| + (-1) = 4(6) + (-1) = 24 - 1 = 23.
So, the correct evaluation is 23, not -6 as you stated.