Don't bail out! 60 points!

this isn't a multiple choice question
this isn't a multiple choice question

(a), (b), and (c) are equations you need to solve, and then tell if it has an infinite number of solutions, one solution, or no solutions.

don't be blind and read it carefully! i've already wasted 120 points in the past 20 minutes.

solve each given equation and show your work. tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.

(a) 3x - 5 + x = 2x - 3 + 2 + 2x
(b) 4x + 5 - 6x = -x +3 -x +2
(c) 8x + 2 - 6 = 4x +8 +3x

Step-by-step explanation:

Problem A

3x - 5 + x = 2x - 3 + 2 + 2x

Bring like terms close to each other so they can be combined on both the  left and right sides.

3x + x - 5 = 2x+ 2x - 3 + 2      Combine like terms

4x - 5 = 4x - 1                          Stop. Nothing more is going to work and give you anything but  No Solution. You will wind up with - 5 = - 1 which is a contradiction.

Number of Solutions: None

Classification:  Contradiction  

Problem B

4x + 5 - 6x = -x + 3 - x + 2 Bring like terms close to each other so they can be combined on both the  left and right sides.

4x - 6x + 5 = -x - x + 3 + 2

-2x + 5 = - 2x + 5               Stop!!!

This will give an infinite number of solutions. Suppose x = 200. Then you will get

-2*200 + 5 = -2 * 200 + 5

- 400 + 5 = - 400 + 5

- 395 = - 395   No matter what you use, the same thing will happen. The equation is an identity. Identities are really useful when you are checking equations. The left side should always come out to be the right side.

Number of Solutions: Infinite

Classication: Identity.

Problem C

8x + 2 - 6 = 4x +8 +3x     Bring like terms close to each other so they can be combined on both the  left and right sides.

8x + 2 - 6 = 4x + 3x + 8     Combine like terms.

8x - 4 = 7x + 8                    Subtract 7x from both sides

8x - 7x - 4 = 7x - 7x + 8      Combine like terms

x - 4 = 8                               Add 4 to both sides

x = 4 + 8

x = 12

Solutions: 1

Classification: Neither. But it is actually classified as a conditional equation if it has 1 legitimate solution.

Note: I really hope I have not wasted your points.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt