Question

GEOMETRY: need some help on these equations, i'm giving a lot of points for this.

Answer 1

1) ML=93

2) GE=58

Explanation:

1)

We want to find ML.

So, we need to find x first.

Note that the entire segment, NK, is the addition of the segments NM, ML, and LK. So:

`NM+ML+LK=NK`

And we know their equations. So, substitute 110+4x for NM, x+103 for ML, 70 for LK, and x+243 for NK. Thus:

`(110+4x)+(x+103)+(70)=x+243`

On the left, combine like terms:

`(4x+x)+(110+103+70)=x+243`

Add:

`5x+283=x+243`

Subtract 283 from both sides:

`5x=x-40`

Subtract x from both sides:

`4x=-40`

Divide both sides by 4:

`x=-10`

So, the value of x is -10.

Substitute this into ML to find it. So:

`ML=(-10)+103`

Add:

`ML=93`

And we're done!

2)

Here, we want to find GE. This means solving for x again.

Note that HF plus FE equates to the entire segment.

HG plus GE also equates to the entire segment.

Thus:

`HF+FE=HG+GE`

Substitute 3x-129 for HF and 4 for FE.

Substitute 13x-993 for HG and 3x-185 for GE. Thus:

`(3x-129)+(4)=(13x-993)+(3x-185)`

Combine like terms on both sides:

`(3x)+(-129+4)=(13x+3x)+(-993-185)`

Add or subtract:

`3x-125=16x-1178`

Add 1178 to both sides:

`3x+1053=16x`

Subtract 3x from both sides:

`1053=13x`

Divide both sides by 13:

`x=81`

So, the value of x is 81.

To find out GE, GE is the 3x-185. So:

`GE=3(81)-185`

Multiply:

`GE=243-185`

Subtract:

`GE=58`

And we're finished!