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

1. For this problem, we are given that EC bisects AD at C. So we can assume that AC and CD are equal. We can set up an equation:

AC = CD

Since AC is given as 3x + 6 and CD is given as 2x + 14, we can set them equal to each other:

3x + 6 = 2x + 14

Now we can solve for x. Subtract 2x from both sides:

x + 6 = 14

Subtract 6 from both sides:

x = 8

Now we can substitute x = 8 back into AC = 3x + 6 to find AC:

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

So the value of x is 8, and the measure of AC is 30.

2. Again, since EC bisects AD at C, we can equate AC and CD:

AC = CD

Given that AC = 5x - 8 and CD = 16 - 3x, we can set them equal:

5x - 8 = 16 - 3x

Add 3x to both sides:

8x - 8 = 16

Add 8 to both sides:

8x = 24

Divide by 8 on both sides:

x = 3

Now, to find AD, we can substitute x = 3 into AC = 5x - 8:

AC = 5(3) - 8
AC = 15 - 8
AC = 7

So the value of x is 3, and the measure of AD is 7.

3. With AD = 6x - 4 and AC = 4x - 3, we can equate them since EC bisects AD at C:

AD = AC

So we set up an equation:

6x - 4 = 4x - 3

Subtract 4x from both sides:

2x - 4 = -3

Add 4 to both sides:

2x = 1

Divide by 2 on both sides:

x = 0.5

Now, to find CD, we substitute x = 0.5 into CD = 2x + 14:

CD = 2(0.5) + 14
CD = 1 + 14
CD = 15

So the value of x is 0.5, and the measure of CD is 15.

4. Given AC = 3x - 1 and AD = 12 - x, we can equate them since EC bisects AD at C:

AC = AD

Setting up the equation:

3x - 1 = 12 - x

Add x to both sides:

4x - 1 = 12

Add 1 to both sides:

4x = 13

Divide by 4 on both sides:

x = 13/4 = -3.25

Now, to find CD, we substitute x = -3.25 into CD = 2x + 14:

CD = 2(-3.25) + 14
CD = -6.5 + 14
CD = 7.5

So the value of x is -3.25, and the measure of CD is 7.5.

1. To find the value of 'x' and the measure of AC, we can set the two given expressions equal to each other:

3x + 6 = 2x + 14

Simplifying the equation, we get:

x = 8

Now, substituting this value of 'x' back into AC = 3x + 6, we can find AC:

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

Therefore, the value of 'x' is 8, and the measure of AC is 30.

2. Similarly, setting AC = CD, we have:

5x - 8 = 16 - 3x

Combining like terms, we get:

8x = 24

Dividing both sides by 8:

x = 3

To find AD, we can substitute this value of 'x' into AC:

AC = 5(3) - 8
AC = 15 - 8
AC = 7

Therefore, the value of 'x' is 3, and AD is 7.

3. Setting AD = AC, we have:

6x - 4 = 4x - 3

Subtracting 4x from both sides, we get:

2x - 4 = -3

Adding 4 to both sides, we have:

2x = 1

Dividing both sides by 2:

x = 0.5

To find CD, substitute this value of 'x' into AC:

CD = 6(0.5) - 4
CD = 3 - 4
CD = -1

Therefore, the value of 'x' is 0.5, and CD is -1.

4. Setting AC = AD, we have:

3x - 1 = 12 - x

Adding 'x' to both sides, we get:

4x - 1 = 12

Adding 1 to both sides, we have:

4x = 13

Dividing both sides by 4, we get:

x = 13/4 = -3.25

To find CD, substitute this value of 'x' into AD:

CD = 12 - (-3.25)
CD = 12 + 3.25
CD = 15.25

Therefore, the value of 'x' is -3.25, and CD is 15.25.

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

x=_______
AC=______
Answer: x=8
AC= 30
yes :)
=============

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..
==========================
5x-8 = 16-3x
8 x = 24
x = 3
AD = 5x-8+16-3x = 15-8+16-9 = 14
or
AD = 2(5x-8) = 30-16 = 14
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3. AD= 6x-4 and AC=4x-3
x=_______
CD______
Answer: x= .5
CD= I'm confused how you do this one too
=============================
6x-4 = 2 (4x-3)
6x-4 = 8x - 6
2 x = 2
x = 1 I get x = 1 not .5
then
CD = AC = 4x-3 = 1
==============================

4. AC=3x-1 and AD= 12-x
x=_____
CD=____
Answer: x= -3.25
CD= I'm have trouble working this one out too
================================
2(3x-1) = 12-x
6 x - 2 = 12 - x
7 x = 14
x = 2 I do not get -3.25
the
CD = AC = 3x-1 = 6-1 = 5