Question

Determine which equations have the same solution set as StartFraction 2 Over 3 EndFraction minus x plus StartFraction 1 Over 6 EndFraction equals 6 x. – x + = 6x by recognizing properties, rather than solving. Check all that apply. 4 – 6x + 1 = 36x StartFraction 5 Over 6 EndFraction minus x equals 6 x – x = 6x 4 – x + 1 = 6x StartFraction 5 Over 6 EndFraction plus x equals 6 x + x = 6x 5 = 30x 5 = 42x

Answer 1

The correct question as understood from the statement is:

Determine which equations have the same solution set as 2/3 – x + 1/6 = 6x by recognizing properties, rather than solving. Check all that apply.

a) 4 - 6x + 1 = 36x

b) 5/6 - x = 6x

c) 4 - x + 1 = 6x

d) 5/6 + x = 6x

e) 5 = 30x

f) 5 = 42x

Answer:

Options: a, b and f

Explanation:

The given equation is:

Adding x to both sides, we get:

Option a) 4 - 6x + 1 = 36x

Moving 6x to the right-hand side of the equation and simplifying the answer, would give us 5 = 42x, which is the same as the second last equation in the above simplification. Thus this equation has the same roots.

Option b) 5/6 - x = 6x

Moving x to another side will give us the same equation as we got in the 3rd last step of the above simplification. Thus this equation has the same roots.

Option c) 4 - x + 1 = 6x

Moving x to another side, and simplifying the result gives us an equation that does not match with the equations in the above simplifications. So, this equation does not have the same root.

Option d) 5/6 + x = 6x

Moving x to another side, and simplifying the result gives us an equation that does not match with the equations in the above simplifications. So, this equation does not have the same root.

Option e) 5 = 30x

This does not match with the second last step of the above simplification. So, this equation does not have the same root.

Option f) 5 = 42x

This equation matches with the second last step of the above simplification. Thus this equation has the same roots.

Answer 2

The correct question as understood from the statement is:

Determine which equations have the same solution set as 2/3 – x + 1/6 = 6x by recognizing properties, rather than solving. Check all that apply.

a) 4 - 6x + 1 = 36x

b) 5/6 - x = 6x

c) 4 - x + 1 = 6x

d) 5/6 + x = 6x

e) 5 = 30x

f) 5 = 42x

Answer:

Options: a, b and f

Explanation:

The given equation is:

`(2)/(3)-x+(1)/(6)=6x`

Adding x to both sides, we get:

`(2)/(3)+(1)/(6)=7x\\\\ (4)/(6)+(1)/(6)=7x\\\\  (5)/(6)=7x\\\\  5=42x\\\\ x=(5)/(42)`

Option a) 4 - 6x + 1 = 36x

Moving 6x to the right hand side of the equation and simplifying the answer, would give us 5 = 42x, which is the same as the second last equation in above simplification. Thus this equation has the same roots.

Option b) 5/6 - x = 6x

Moving x to other side will give us the same equation as we got in 3rd last step of the above simplification. Thus this equation has the same roots.

Option c) 4 - x + 1 = 6x

Moving x to other side, and simplifying the result gives us an equation which does not match with the equations in above simplifications. So, this equation does not have the same root.

Option d) 5/6 + x = 6x

Moving x to other side, and simplifying the result gives us an equation which does not match with the equations in above simplifications. So, this equation does not have the same root.

Option e) 5 = 30x

This does not match with the second last step of the above simplification. So, this equation does not have the same root.

Option f) 5 = 42x

This equation matches with the second last step of the above simplification. Thus this equation has the same roots.