Question

Can someone help asap I can't figure this out and I lost my notes

The following is a student solution to the inequality

5/12-(x-3)/6≤(x-2)/3

5/12-2/2*(x-3)/6≤4/4*(x-2)/3

5/12-(2x-6)/12≤(4x-8)/12

5-2x-6≤4x-8

-1-2x≤4x-8

-6x≤-9

x≥3/2

There are two mathematical errors in this work. Identify at what step each mathematical error occurred and explain why it is mathematically incorrect.

The first mathematical error occurred going from line ____ to line ____.

Why it is incorrect:


The second mathematical error occurred going from line ____ to line ____.


Why it is incorrect:



Solve the inequality correctly.















Question 2(5 points) Same Solutions?
Which of the following equations have the same solution? Give reasons for your answer that do not depend on solving the equations.
-(7-4x)=9

12=-4(-6x-3)

5x+34=-2(1-7x)

14=-(x-8)

-8=-(x+4)

x+5=-5x+5

Answer 1

Question 1:

The first error occured going from line 3 to line 4.

Why its incorrect:

instead of " ... -(2x-6) ... --> .... -2x + 6 .. .", he writes that

" ... -(2x-6) ... --> .... -2x - 6 .. .". In other words he multiplied by -1 without changing the sign.

The second error can be found going from line 5 to line 6.

Why its incorrect:

- 1 - 2x ≤ 4x - 8

- 1 - 2x + 1 ≤ 4x - 8 + 1

-2x ≤ 4x - 7

-2x -4x ≤ 4x - 4x - 7

-6x ≤ -7

Solving the inequality correctly:

5/12-(x-3)/6≤(x-2)/3

5/12-2/2*(x-3)/6≤4/4*(x-2)/3

5/12-(2x-6)/12≤(4x-8)/12

5-2x+6≤4x-8

11-2x≤4x-8

11 + 8≤ 4x + 2x

6x ≥ 19

x ≥ 19/6

Answer 2

Question 1:

The first error occurred going from line 2 to line 3. It is wrong because 6 was multiplied by 2 while 4/4*(x-2)/3 was not.

The second error occurred going from line 5 to line 6. It is wrong because while taking -1 to the other side, it becomes +1, and -8 + 1 = -7, not -9.

Question 2:

Equations 1, 3 and 5 have the same solution 4 and equations 2 and 6 have the same solution 0.

-(7-4x)=9

4x-7=9

4x=9+7

4x=16

x=4

12 = -4(-6x-3)

12/-4 = -6x-3

-3 = -6x-3

-6x=0

x=0

5x + 34 = -2(1-7x)

5x + 34 = 14x - 2

9x - 36 = 0

9x = 36

x = 4

14 = -x + 8

x=8-14

x=-6

-8 = -x-4

x = -4 +8

x=4

x + 5 = -5x + 5

6x = 0

x = 0