Question

1.) A.) Name the 'item' on which point L exists.B.) If ML= 6x - 4, LH = 10x+1 and MH = 29, find the length of ML.

Answer 1

Now for the point A), L is in the middle of M and H, and the interval will be:

$(M,H)$

For the second point, We need to put the value of the segments in the draw...

From the draw, we can deduce that:

$ML+LH=MH$

We replace with values:

$\begin{gathered} ML+LH=MH \\ 6x-4+(10x+1)=29 \end{gathered}$

We solve to x:

$\begin{gathered} 6x-4+(10x+1)=29 \\ 6x\text{ -4 +10x +1=29 ; we agroup the values with x} \\ (6x+10x)-4+1=29 \\ 16x-3=29 \\ 16x=29+3 \\ 16x=32 \\ x=\frac{32}{16}=2 \\ x=2 \end{gathered}$

Finally, if the value of x = 2, then whi can replace in:

$\begin{gathered} ML=6x-4 \\ ML=6(2)-4 \\ ML=12-4 \\ ML=8 \end{gathered}$

Your answer of point B) is ML=8.