Answer:
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:
<u>Step 1: Making the denominators common for all fractions</u>
This step is done correctly in the given solution.
<u>Step 2: Simplifying </u>
This step is done correctly in the given solution
<u>Step 3: Multiplying both sides by 12, and simplifying.</u>
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.
<u>Step 4: Simplification:</u>
<u>Step 5: Moving Common terms to one side and simplifying</u>
Error was made in this step. When a number is moved to other side, its sign will be changed.
<u>Step 6: Dividing both sides by -6</u>
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)