Question

Beth is solving this equation: 1/x + 3 =3/x

she says "I can multiply both sides by X and get the linear equation 1 + 3x = 3 whose solution is x = 2/3 ."
which of the following statements makes this a correct argument, or shows that it is in correct? Select all that apply.

a. you cannot multiply both sides by x because you do not know what x is.

b. you can assume x = 0 because both sides are undefined if x = 0

c. after multiplying both sides by X you need to subtract 1 from both sides.

d. the equation is not linear, so you cannot use the methods normally used for solving linear equations.

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Answer 1

a. you cannot multiply both sides by x because you do not know what x is.

Explanation:

Given:

`(1)/(x) + 3 = (3)/(x)`

Required

Select which of the option that applies

Considering (a):

A is incorrect:

Because: Multiplying both sides by x has nothing to do with whether the value of x is known or not

Considering (b):

B is incorrect:

Substitute 0 for x in the given expression

`(1)/(0) + 3 = (3)/(0)`

`Und efi ned`

Both sides of the equation are undefined

However, you cannot assume x to be 0

Considering (c):

C is correct:

Start by multiplying both sides by x

`x ((1)/(x) + 3) = (3)/(x) * x`

`1 + 3x = 3`

Then, subtract 1 from both sides

`1 - 1 + 3x = 3 - 1`

`3x = 2`

Divide through by 3

`x = (2)/(3)`

Considering (d):

D is incorrect;

Because, the equation is linear