Points EC bisects points AD at C. For each of the following, find the value of 'x' and the measure of the indicated segment. Please correct me if I'm wrong!

1. AC= 3x+6 and CD=2x+14
x=_______
AC=______
Answer: x=8
AC= 30

2. AC= 5x-8 and CD=16-3x
x=______
AD=_____
Answer: x=3
What will AD be because I'm sooo confused on how to work it out..

3. AD= 6x-4 and AC=4x-3
x=_______
CD______
Answer: x= .5
CD= I'm confused how you do this one too

4. AC=3x-1 and AD= 12-x
x=_____
CD=____
Answer: x= -3.25
CD= I'm have trouble working this one out too

*How do you find the measurement of the segments? Someone please walk me thorough on how to do it. I get how to find x but not the segments on #'s 2-4!

Did you draw a diagram?

AC = CD
AD = AC+CD

#1 ok
#2. The calculation for x is just as in #1.
AD = AC+CD = 7+7 = 14

#3. AD=AC+CD = 2(AC), so
6x-4 = 2(4x-3)
x = 1
CD = 1
#4. As in #3,
12-x = 2(3x-1)
x = 2
CD = 5

To find the value of 'x' and the measure of the indicated segment, we will set up equations for each problem and solve them step-by-step.

1. AC = 3x + 6 and CD = 2x + 14

Since EC bisects AD at C, this means AC is equal to CD. Therefore:

3x + 6 = 2x + 14

To solve for x, we subtract 2x from both sides:

3x - 2x + 6 = 2x - 2x + 14

x + 6 = 14

Next, we subtract 6 from both sides:

x + 6 - 6 = 14 - 6

x = 8

To find the value of AC:

AC = 3x + 6 = 3(8) + 6 = 24 + 6 = 30

So, x = 8 and AC = 30.

2. AC = 5x - 8 and CD = 16 - 3x

Since EC bisects AD at C, AC is equal to CD:

5x - 8 = 16 - 3x

To solve for x, we add 3x to both sides:

5x + 3x - 8 = 16 - 3x + 3x

8x - 8 = 16

Next, we add 8 to both sides:

8x - 8 + 8 = 16 + 8

8x = 24

Now, we divide both sides by 8:

(8x)/8 = 24/8

x = 3

To find the measure of AD, substitute the value of x into AC:

AD = 5x - 8 = 5(3) - 8 = 15 - 8 = 7

So, x = 3 and AD = 7.

3. AD = 6x - 4 and AC = 4x - 3

Since EC bisects AD at C, AC is equal to CD:

6x - 4 = 4x - 3

To solve for x, we subtract 4x from both sides:

6x - 4 - 4x = 4x - 3 - 4x

2x - 4 = -3

Next, we add 4 to both sides:

2x - 4 + 4 = -3 + 4

2x = 1

Now, we divide both sides by 2:

(2x)/2 = 1/2

x = 0.5

To find the measure of CD, substitute the value of x into AC:

CD = 4x - 3 = 4(0.5) - 3 = 2 - 3 = -1

So, x = 0.5 and CD = -1.

4. AC = 3x - 1 and AD = 12 - x

Since EC bisects AD at C, AC is equal to CD:

3x - 1 = 12 - x

To solve for x, we add x to both sides:

3x + x - 1 = 12 - x + x

4x - 1 = 12

Next, we add 1 to both sides:

4x - 1 + 1 = 12 + 1

4x = 13

Now, we divide both sides by 4:

(4x)/4 = 13/4

x = -3.25

To find the measure of CD, substitute the value of x into AC:

CD = 3x - 1 = 3(-3.25) - 1 = -9.75 - 1 = -10.75

So, x = -3.25 and CD = -10.75.

To find the measurements of the segments, substitute the value of 'x' into the given expressions for AC and CD.

To find the value of 'x' and the measure of the indicated segment, we will use the fact that line segment EC bisects line segment AD at point C. This means that AC is equal to CD.

Let's go through each question step by step:

1. AC = 3x + 6 and CD = 2x + 14
Since line segment EC bisects line segment AD, AC = CD.
Therefore, we can set up an equation:
3x + 6 = 2x + 14
Simplifying this equation, we get:
x = 8

To find the measure of segment AC, substitute x = 8 into the expression AC = 3x + 6:
AC = 3(8) + 6
AC = 30

So, for question 1, x = 8 and AC = 30.

2. AC = 5x - 8 and CD = 16 - 3x
Again, since line segment EC bisects line segment AD, we know that AC = CD.
Set up an equation:
5x - 8 = 16 - 3x
Simplifying:
8x = 24
x = 3

To find the measure of segment AD, substitute x = 3 into the expression AD = 5x - 8:
AD = 5(3) - 8
AD = 15 - 8
AD = 7

So, for question 2, x = 3 and AD = 7.

3. AD = 6x - 4 and AC = 4x - 3
Again, AC = CD since line segment EC bisects line segment AD.
Set up an equation:
6x - 4 = 4x - 3
2x = 1
x = 0.5

To find the measure of segment CD, substitute x = 0.5 into the expression CD = 2x + 14:
CD = 2(0.5) + 14
CD = 1 + 14
CD = 15

So, for question 3, x = 0.5 and CD = 15.

4. AC = 3x - 1 and AD = 12 - x
Once again, since line segment EC bisects line segment AD, AC = CD.
Set up an equation:
3x - 1 = 12 - x
4x = 13
x = -3.25

To find the measure of segment CD, substitute x = -3.25 into the expression CD = 2x + 14:
CD = 2(-3.25) + 14
CD = -6.5 + 14
CD = 7.5

So, for question 4, x = -3.25 and CD = 7.5.

In summary:
- For each question, find the value of 'x' by setting the expressions for AC and CD equal to each other.
- After finding 'x', substitute it into the expression for AC to find the measure of that segment.
- To find the measure of segment CD, substitute 'x' into the expression for CD.