Which of the following inequalities is correct?1: -9 ≥ -72: -10 > |-10|3: 6 ≤ |-6|4: 0 < -13

4 answers
Question:

Which of the following inequalities is correct? 1: -9 ≥ -7
2: -10 > |-10|
3: 6 ≤ |-6|
4: 0 < -13

Answers

It should be 2 but I mean I not for sure tho

i only know question one so here

The first mathematical error occurred going from line __3__ to line _4___.

Why it is incorrect:  

It is incorrect because the minus sign was not properly distributed. Line 4 should be ...

 5 -2x +6 ≤ 4x -8

a.  

The second mathematical error occurred going from line ___5_ to line 6.

Why it is incorrect:

It is incorrect because 1 was added on the left and subtracted on the right. The same number needs to be added or subtracted on both sides.

 

b.Solve the inequality correctly.

 5 -2x +6 ≤ 4x -8correct line 4

11 -2x ≤ 4x -8 combine constants

  19 -2x ≤ 4x add 8

  19 ≤ 6x add 2x

19/6 ≤ x divide by 6

1)

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

2)

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

Step-by-step explanation:

Question 1)

The given inequality is:

[tex]\frac{5}{12}-\frac{x-3}{6} \leq \frac{x-2}{3}[/tex]

Step 1: Making the denominators common for all fractions

[tex]\frac{5}{12}-\frac{2}{2} \times \frac{x-3}{6} \leq \frac{4}{4} \times \frac{x-2}{3}[/tex]

This step is done correctly in the given solution.

Step 2: Simplifying

[tex]\frac{5}{12}-\frac{2x-6}{12}\leq \frac{4x-8}{12}[/tex]

This step is done correctly in the given solution

Step 3: Multiplying both sides by 12, and simplifying.

[tex]5-(2x-6)\leq 4x-8\\\\ 5-2x+6\leq 4x-8[/tex]

First error is made in this step. While opening the brackets, the negative sign should be distributed inside the bracket, which will change the signs.

Step 4: Simplification:

[tex]11-2x\leq 4x-8[/tex]

Step 5: Moving Common terms to one side and simplifying

[tex]-2x-4x\leq -8-11\\\\ -6x\leq -19[/tex]

Error was made in this step. When a number is moved to other side, its sign will be changed.

Step 6: Dividing both sides by -6

[tex]x\geq \frac{19}{6}[/tex]

Conclusion:

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

Question 2:

In the Equation 2: 12=-4(-6x-3), when -4 will be multiplied inside the brackets, the 12 on eft hand side will cancel the 12 that will appear on right hand side, giving a result that will lead to x = 0.

Same is the case with Equation 6: x+5=-5x+5, 5 on both sides will cancel out leaving x = 0.

So, 2nd and 6th equations will have the same solution.

In Equation 1, on expanding the bracket and moving 7 to other side, we get a relation: 4x = 16

In Equation 3, on simplifying the right hand side, and carrying common terms to one side, we get the relation: - 9x = -36

In Equation 5, on expanding the bracket and simplifying the relation is reduced to 4 = x

It can be observed that all these 3 equations have the same solution i.e. x = 4

So, the following set of Equations have the same solution:

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

QUESTION 1

The first mathematical error occurred going from line 3 to line 4.

Why it is incorrect: distributive property of multiplication is not well applied

-(2x-6) = -2x+6

The second mathematical error occurred going from line 5 to line 6.

Why it is incorrect: the "-1" should had passed as "+1" from the left side to the right side of the inequality

-1-2x≤4x-8

-2x-4x≤-8+1

-6x≤-7

QUESTION 2

To answer this question we have to rewrite the equations in a similar way, as follows:

-(7-4x)=9

7-4x = -9

-4x+16=0 (eq. 1)

12=-4(-6x-3)

12=24x+12

0=24x (eq. 2)

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

5x+34=-2+14x

-9x+36 = 0 (eq. 3)

if you multiply equation 1 by 9/4, you get equation 3, then they have the same solution

14=-(x-8)

14=-x+8

x+6=0 (eq. 4)

-8=-(x+4)

-8=-x-4)

x-4 = 0 (eq. 5)

if you divide equation 1 by -4, you get equation 5, then they have the same solution

x+5=-5x+5

6x=0 (eq. 6)

if you divide equation 2 by 4, you get equation 6, then they have the same solution.

b.

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

-6x≤-19

x≥19/6

Similar Solved Works

4 answers

Moishe the Beadle's identity has been shaped by the experiences he has gone through.Explain whether

Moishe the Beadle's identity has been shaped by the experiences he has gone through. Explain whether you agree or disagree. Use the CERER Framework to answer in 5-7 sentences....
8 answers

The blue shape is a dilation of the black shape. What is the scale factor of the dilation? I need the coorect answer

The blue shape is a dilation of the black shape. What is the scale factor of the dilation? I need the coorect answer [tex]The blue shape is a dilation of the black shape. What is the scale factor of the dilation? I need t[/tex]...
10 answers

The image below shows the distribution of members of a population. What type of distribution is shown? A. Clumped B. Irregular

The image below shows the distribution of members of a population. What type of distribution is shown? A. Clumped B. Irregular C. Uniform D. Random [tex]The image below shows the distribution of members of a population. What type of distribution is show[/tex]...
10 answers

I'll give ! instructions: select the correct text in the passage. which sentence shows that sebastien will need to attend

I'll give ! instructions: select the correct text in the passage. which sentence shows that sebastien will need to attend entrance counseling and sign a promissory note? [sebastien wants to take a certificate course in computer graphics.] he has a brother who is in junior high school. although seb...
3 answers

How does melville indirectly characterize ahab in the opening paragraphs of the excerpt?

How does melville indirectly characterize ahab in the opening paragraphs of the excerpt? how is this characterization consistent with romanticism, and how does it resemble some of hawthorne’s characterization from the scarlet letter? : !...
4 answers

The chemical equation describing the burning of hydrogen gas is: 2H2 + O2 ---> 2H2O.Why is this both a synthesis and a combustion reaction?

The chemical equation describing the burning of hydrogen gas is: 2H2 + O2 ---> 2H2O. Why is this both a synthesis and a combustion reaction?...
4 answers

Write and slove an inequality that models that sitiution to determine the maximum number of bags fruit, b, harper can buy. Harper

Write and slove an inequality that models that sitiution to determine the maximum number of bags fruit, b, harper can buy. Harper has $30 to spend at the grocery store she’s going to buy bags for $3.25 each and one box of crackers that cost $4.25....
4 answers

Using complete sentences, explain which function has the greatest y-intercept.

Using complete sentences, explain which function has the greatest y-intercept. [tex]Using complete sentences, explain which function has the greatest y-intercept.[/tex]...
10 answers

Can someone explain how it is 1?

Can someone explain how it is 1? [tex]Can someone explain how it is 1?[/tex]...
3 answers

What does the word pitiful connote or suggest about Tavi's bicycle?A. It is worthy of sympathy or pity.B. It is unimpressive compared

What does the word pitiful connote or suggest about Tavi's bicycle? A. It is worthy of sympathy or pity. B. It is unimpressive compared to a car. C. It is very old and in need of repair. D. It won't help Tavi get to downtown....
4 answers

According to the general equation for conditional probability, if P(An B) = 4/5and P(B) = 5/6 what is P(AIB)?

According to the general equation for conditional probability, if P(An B) = 4/5 and P(B) = 5/6 what is P(AIB)?...
3 answers

What evidence of shamanism, animism, and ancestor worship are found in modern Japan? Describe at least two specific examples to support your response.

What evidence of shamanism, animism, and ancestor worship are found in modern Japan? Describe at least two specific examples to support your response....
10 answers

The table below shows a proportional relationship between s and t

The table below shows a proportional relationship between s and t...
4 answers

Lenz’s law states that the induced emf opposes the change in the magnetic field. imagine you were actually turning the

Lenz’s law states that the induced emf opposes the change in the magnetic field. imagine you were actually turning the water wheel by hand to generate current. would the wheel resist motion? as you worked harder at moving the wheel, you would exp...
4 answers

If m angle a is 155 degrees what is m angle c?

If m angle a is 155 degrees what is m angle c?...
7 answers

5(4x – 2x) + 12 = 4x – 2

5(4x – 2x) + 12 = 4x – 2...
4 answers

What roles did religion and race play in slavery according to the 1705 Slave Codes?

What roles did religion and race play in slavery according to the 1705 Slave Codes?...
1 answer

What evidence shows that the alliance of antony, lepidus, and octavius could fail? discuss three details

What evidence shows that the alliance of antony, lepidus, and octavius could fail? discuss three details from scene 1 in your answer. (from the tragedy of julius caesar)...
10 answers

Name the process in which a cell develops new sub-cellular structures to let it perform a specific function:

Name the process in which a cell develops new sub-cellular structures to let it perform a specific function:...
3 answers

Consider the balanced reaction below:2N205 → 4NO2 + O2How many moles of N205 are neededto produce 7.90 g of NO2?[?] moles N205

Consider the balanced reaction below: 2N205 → 4NO2 + O2 How many moles of N205 are needed to produce 7.90 g of NO2? [?] moles N205...

-- 0.017201--