Could someone please check my math questions? any help will be greatly appreciated!

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

v\4. Solve:

5|2x + 1 | = 55
Divide both side by 5: |2x+1|=11
###Now subtract 1 from each side
###2x=10
###Now divide each side by 2
### x=5 I have no clue what your teacher meant.

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 ### Correct

4x-8=20 or -4x+8=20
### steps missing here, you did it in your head.
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)|
***-3*6= -18
=-1(-6)=-6
Answer is -6
What my teacher said was wrong~~ incorrect substitution at the end

Thank you soo much!! I really appreciate your help!

To check your math questions, let's go through the steps and see if there are any mistakes:

4. Solve:
5|2x + 1| = 55

To solve this equation, you correctly divided both sides of the equation by 5, which gives you:
|2x + 1| = 11

Next, you wrote down the two possibilities for the absolute value:
2x + 1 = 11 (equation 1)
2x + 1 = -11 (equation 2)

However, you made a mistake when adding 1 to both sides of equation 1 and equation 2. It should be:
2x = 10 (equation 1)
2x = -12 (equation 2)

Now, solving for x:
From equation 1, you correctly divided both sides by 2, which gives you:
x = 5

From equation 2, you correctly divided both sides by 2, which gives you:
x = -6

So, the correct solutions are x = 5 and x = -6.

5. Solve:
1/2|4x – 8| - 7 = 3

To solve this equation, you correctly started by multiplying both sides by 2:
|4x - 8| = 20

Next, you set up the two possibilities for the absolute value:
4x - 8 = 20 (equation 1)
4x - 8 = -20 (equation 2)

To solve for x, you need to add 8 to both sides of both equations. You correctly did this:
4x = 28 (equation 1)
4x = -12 (equation 2)

Now, solving for x:
From equation 1, you correctly divided both sides by 4, which gives you:
x = 7

From equation 2, you correctly divided both sides by 4, which gives you:
x = -3

So, the correct solutions are x = 7 and x = -3.

6. Evaluate the given expression when a = 3, b = -3, c = 4, and d = -1.
c|a-b| + d

To evaluate this expression, you correctly substitute the given values:
c|a - b| + d = 4|3 - (-3)| + (-1)

Now, simplify the expression inside the absolute value:
c|a - b| + d = 4|6| + (-1)

Next, evaluate the absolute value:
c|a - b| + d = 4 * 6 + (-1)

Multiply and add:
c|a - b| + d = 24 + (-1)

Finally:
c|a - b| + d = 23

So, the correct answer is 23.

Overall, it seems like you made some mistakes in your teacher's corrections. The solutions and evaluations you provided were mostly correct. Make sure to double-check the steps during the solving process and the substitution of values.