Question

5. Which of the following is a linear equation?
PLEASE HELPP!!

Answer 1

B

Explanation:

Linear equation with one variable has the form of
`ax+b=0`

Since when you simplify you get
`0=(11)/(3)x+18`

Answer 2

The linear equation is Option B

Explanation:

The concept related to this question is this:

A linear equation is an equation that the exponent of the all of the variables in the equation is 1

Therefore a linear equation doesn´t have square root (like Option A), cuadratic expressions (like Option D), and the variable isn't dividing coefficients (like Option C)

We have analyze every option in order to apply this concept and find the right answer

Option A:
`√(x) + 14=15 x`

In this equation, the square root contains one of the variable.

Now, a square root can be expressed as a fractional exponent, following this rule:

`\sqrt[n]{x} = x^{(1)/(n)}`

For a square root:

`n = 2`

Therefore:

`√(x) =x^{(1)/(2)}`

And the equation can be written in this way:

`x^{(1)/(2)}+14=15x`

Like in this equation has one of its variables with an exponent different than 1, this option isn't a linear equation

Option B:
`(10)/(3)x-3=7x+15`

In this case the exponents of all of the variables are 1, therefore this option is a linear equation

Option C:
`(10)/(3)x-3=(7)/(x)+15`

In this case there is a variable dividing a coefficient, therefore its exponent follows this rule:

`(1)/(x) = x^(-1)`

Therefore, the equation can be written in this way:

`(10)/(3)x-3=7x^(-1)+15`

Therefore, the exponent of this variable is different than 1, this option isn't a linear equation

Option D:
`3x^(2) +10x=5`

In this case the exponent of the first variable is different than 1 (
`3x^(2)`), therefore this option isn't a linear equation