Question

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

Answer 1

Answer:

1) ML=93

2) GE=58

Step-by-step 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!