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I need serious help, this is hard

I need serious help, this is hard-example-1

1 Answer

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Answer: 58

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Step-by-step explanation:

M is the midpoint of segment PQ. This means PQ is cut in half into two equal smaller pieces PM and MQ. We can say that PM = MQ.

Furthermore, we can say that PQ is twice as long as either piece, so

  • PQ = 2*PM
  • PQ = 2*MQ

We'll use the second equation to say the following:

PQ = 2*MQ

6x+56 = 2*MQ .... replace PQ with 6x+56

6x+56 = 2*(5x+8) .... replace MQ with 5x+8

6x+56 = 2*5x + 2*8 .... distribute

6x+56 = 10x+16

6x+56-10x = 16 .... subtract 10x from both sides

-4x+56 = 16

-4x = 16-56 ..... subtract 56 from both sides

-4x = -40

x = -40/(-4) ..... divide both sides by -4

x = 10

Once we know the value of x, we use it to find the length of PM

PM = MQ

PM = 5x+8

PM = 5*10+8

PM = 50+8

PM = 58

Note how PQ = 6x+56 = 6*10+56 = 116 is exactly twice as large compared to 58. In other words, 2*58 = 116. This confirms that PQ is twice as long compared to PM or MQ. This helps confirm we have the right answer.