Answer:
(1) 2x - 6 < - 14
(2) 2x + 3 < 1
Explanation:
(1) 2x - 6 < -14 -> 2x < - 8 -> x < - 4
(2) 2x + 3 < 1 -> 2x < -2 --> x < -1
Compound solution set: x < - 4
==========|-4----------|-1-------|0----------------
Step-by-step explanation:
To determine the lengths of the sides from shortest to longest, you need to calculate the corresponding angles. The higher angles will correspond to longer sides.
To find the angles, you have to solve for x. You’re already given that angle A is 76. To find the others, you know that angle C is 180-(16x+16) since it’s supplemental to the exterior angle. Then, you know the sum of the angles of the entire triangle is 180, so add up A, B, and C
A+B+C=180
76+6x+(180-16x-16)=180
240-10x=180
-10x=-60
x=6
So to find angle B, you use 6x or 6(6)=36.
To find angle C, you use 180-(16x-16) or 180-16(6)-16=68
So now match up the angles with their corresponding sides to find the length from shortest to longest.
Angle A (76) corresponds with BC
Angle B (36) corresponds with AC
Angle C (68) corresponds with AB
Again, the higher the degree, the longer the corresponding side, so AC is shortest, AB is next, and BC is the longest.
The like terms are the a terms and the constants. If you combine them, you will get 24, as the negative a and the positive a cancel each other out.
This question is checking to see if you remember what the three angles
of any triangle always add up to. Apparently you don't, or you would not
need to go out looking for somebody who does.
The three angles inside every triangle always add up to 180° .
If two of them add up to 135° , then that leaves
(180° - 135°) = 45° .
for the one remaining angle.
