Question

I need help with this problem it's a two-part thing

Answer 1

To find PQ, notice that M divides PQ into two parts with the same measure.

So, we have:

`10x+3=14x-13`

Now, we can solve the above equation for x, and then find PQ.

To solve the equation, we can apply the same operations on both sides of the equation, until we isolate the variable x and find its value:

`\begin{gathered} 10x+3-14x=14x-13-14x \\ \\ -4x+3=-13 \\ \\ -4x+3-3=-13-3 \\ \\ -4x=-16 \\ \\ (-4x)/(-4)=(-16)/(-4) \\ \\ x=4 \end{gathered}`

So, using x = 4, we obtain:

`\begin{gathered} PQ=2\cdot(10x+3) \\ \\ PQ=2\cdot(10\cdot4+3) \\ \\ PQ=2\cdot(40+3) \\ \\ PQ=2\cdot43 \\ \\ PQ=86 \end{gathered}`

Therefore, PQ = 86.