Question

If R is the midpoint of QS, RS = 2x-4, ST = tx-1, and RT = 8x-43

Answer 1

Answer: x = 1

Step-by-step explanation:

I have no idea what the actual answer is, as you didn't ask a question. So i'm assuming that you want the value of x.

Step 1: Draw a line containing all the points

R is in between point Q and point S, while T is last, based on alphabetical order.

Illustration:

2x - 4 Tx - 1

Q R S T

8x - 43

Step 2: Find T's value

To find t, create the substitution equation RS + ST = RT

2x - 4 + tx - 1 = 8x - 43

-2x -2x

-4 + tx - 1 = 6x - 43

tx - 5 = 6x - 43

tx = 6x - 38

tx/x = 6x/x - 38

t = 6 - 38

t = -32

This is the value of t

By the way, there is no correlation between point T and the variable t.

Step 3: Find x's value

Now that we know what t is, we can solve for x

2x - 4 -32x - 1 = 8x - 43

-30x - 5 = 8x - 43

+30x +30x

-5 = 38x - 43

+43 +43

38 = 38x

38/38 = 38x/38

1 = x

This is the value of x

Answer 2

The question is incomplete. Here is the complete question.

If R is the midpoint of QS,
`RS=2x-4`, ST =
`4x-1` and RT =
`8x-43`, find QS.

Answer: QS = 68 units

Explanation: The figure below shows a line segment QT.

To determine QS, first, determine value of x:

RT = RS + ST

`8x-43=2x-4+4x-1`

`8x-43=6x-5`

2x = 38

x = 19

Now, we determine QS:

Midpoint is a point dividing a line segment in two equal parts.

Then, QR = RS.

QS = QR + RS

QS = 2RS

`QS=2(2x-4)`

`QS=4x-8`

Substituting x = 19:

`QS=4.19-8`

QS = 68

The segment QS is 68 units.