7. A is the midpoint of CT. CA = 7x - 5, CT = 46, find x.

From the question given above, we were told that A is the midpoint of CT. This simply implies that CA and AT are equal.

Thus,

With the above information in mind, we can obtain the value of x as follow:

CA = 7x - 5

CT = 46

AT = CA

CT = CA + AT

CT = CA + CA

CT = 2CA

46 = 2(7x - 5)

Divide both side by 2

46/2 = 2(7x - 5)

23 = 7x - 5

Collect like terms

23 + 5 = 7x

28 = 7x

Divide both side by 7

x = 28/7

Therefore, the value of x is 4

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The correct answer is x = 4.

Step-by-step explanation:

If A is the midpoint of CT, this means that CA is equal to AT.  This also lets us know that CA is half of CT.  This lets us write the following equation:

CA = 1/2(CT)

Now, we can substitute the values we are given into the equation above.

7x - 5 = 1/2 * (46)

If we simplify the right side of the equation, we get:

7x - 5 = 23

The next step is to add 5 to both sides of the equation.  This gives us:

7x = 28

Finally, we can divide both sides of the equation by 7.

x = 4

Therefore, the answer is x = 4.

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