If t is the midpoint of su, find x. ( st=8x+11 and tu= 12x-1)

Using the midpoint concept, it is found that x = 3

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Since they are equal, we can solve for x.

x = 3 is the answer.

A similar problem is given at link

Explanation:

T is the midpoint of SU, so point T cuts segment SU into two equal halves. Those two halves being ST and TU, therefore, ST = TU

ST = TU

8x+11 = 12x-1 ... substitution

8x+11-8x = 12x-1-8x ... subtract 8x from both sides

11 = 4x-1

11+1 = 4x-1+1 add 1 to both sides

12 = 4x

4x = 12

4x/4 = 12/4 divide both sides by 4

x = 3

As a check, plug x = 3 into each equation below

ST = 8x+11 = 8*3+11 = 24+11 = 35

TU = 12x-1 = 12*3-1 = 36-1 = 35

Each piece ST and TU is 35 units long. So this confirms we have the right answer.