Question

Choose the linear equations from the following. Identify L.H.S and R.H.S separately and write them in the weighing balance shown below. Also justify that why the other equations are not linear equations? 3 x – 2 > 42, 5 – 2 x2 + 7 = 54, -4p3 + 2p – 7 = 5, 2 y – 6 = y + 9​

Answer 1

Answer:

From the given equations, 2 y – 6 = y + 9​ is linear equation where LHS = y and RHS = 15

Step-by-step explanation:

Linear equations are equations of the form y=mx+b. involving only a constant (b) and a first-order (linear) term. This means, these equations should have terms only with a single power.

The given expressions are,

3 x – 2 > 42

5 – 2 x2 + 7 = 54

-4p3 + 2p – 7 = 5

2 y – 6 = y + 9​

Let's see which are linear equations,

i) 3 x – 2 > 42

Here we see only terms with single power, but this is not an equation since it does not have '=' sign. It has a 'greater than' sign. Therefore this is an example of linear in-equation.

ii) 5 – 2 x2 + 7 = 54  

Re-writing the equation,

$5 - 2x^{2} +7= 54$

Since this has square, it is not of single power. Therefore this is not a linear equation.

iii) -4p3 + 2p – 7 = 5

Re-writing the equation,

$-4p^{3} +2p-7=5$

Since this has a cube, it is not of single power. Therefore this is not a linear equation.

iv)2 y – 6 = y + 9​

Here we find all terms are of single power, hence this is a linear equation.

Let's simplify and find LHS and RHS,

we have, 2 y – 6 = y + 9​

subtracting y from both sides we get,

2 y – 6 – y = y + 9​– y

i.e, y-6=9

Now adding 6 on both sides,

y-6+6 = 9+6

y = 15

This is the simplifies form, where LHS = y and RHS = 15