Question

Which of the following is not a linear equation?
a)7/3x - 5 = 4x -3
b)x² + 5 = 3x-5
c)3x + 3 = 5x + 2
d)(x + 2)² = x² - 8​

Answer 1

Answer:

Which of the following is not a linear equation?

a)7/3x - 5 = 4x -3

b)x² + 5 = 3x-5

c)3x + 3 = 5x + 2

d)(x + 2)² = x² - 8​

Step-by-step explanation:

a) on solving=> 7-15 x= 12 x- 9  

                        27 x - 16 = 0     this is  a linear equation (degree of x is 1)

b) x^2 + 5 -3 x + 5 = 0

   x^2 - 3 + 10 = 0     This is also not a linear equation since it is quadratic equation. (degree of x is 2)

c) 3 x + 3 - 5 x -2 =0

    -2 x + 1 = 0

     2 x -1 = 0       This is a linear equation  (degree of x is 1)

d) x^2 + 4 x + 4 - x^2 + 8 = 0

     4 x + 12 = 0    this is a linear equation (degree of x is 1)

so, option b is not a linear equation

Answer 2

Given,

Which of the following is not a linear equation?

$\[\begin{array}{l}\left( a \right)\frac{7}{3}x - 5 = 4x - 3\\\left( b \right){x^2} + 5 = 3x - 5\\\left( c \right)3x + 3 = 5x + 2\\\left( d \right){\left( {x + 2} \right)^2} = {x^2} - 8\end{array}\]$

To find,

The non-linear equation from the given options.

Solution,

Know that a linear equation is one that has a degree $\[1.\]$

Evaluate option (a).

$\[\begin{array}{l} \Rightarrow \frac{7}{3}x - 5 = 4x - 3\\ \Rightarrow \frac{7}{3}x - 4x = 5 + 3\\ \Rightarrow - \frac{5}{4}x = 8\\ \Rightarrow x = - \frac{{32}}{5}\end{array}\]$

Understand that here the degree is $\[1\]$, hence, it is a linear equation.

Evaluate option (b).

$\[\begin{array}{l} \Rightarrow {x^2} + 5 = 3x - 5\\ \Rightarrow {x^2} + 5 - 3x + 5 = 0\\ \Rightarrow {x^2} - 3x + 10 = 0\end{array}\]$

Understand that here the degree is $\[2\]$, hence, it is not a linear equation.

Evaluate option (c).

$\[\begin{array}{l} \Rightarrow 3x + 3 = 5x + 2\\ \Rightarrow 5x - 3x = 3 - 2\\ \Rightarrow 2x = 1\\ \Rightarrow x = \frac{1}{2}\end{array}\]$

Understand that here the degree is $\[1\]$, hence, it is a linear equation.

Evaluate option (d).

$\[\begin{array}{l} \Rightarrow {\left( {x + 2} \right)^2} = {x^2} - 81\\ \Rightarrow {x^2} + 4 + 4x = {x^2} - 81\\ \Rightarrow {x^2} - {x^2} + 4x = - 81 - 4\\ \Rightarrow 4x = - 85\end{array}\]$

Understand that here the degree is $\[1\]$, hence, it is a linear equation.

Hence, the correct option is (b) i.e.$\[{x^2} + 5 = 3x - 5.\]$