Question

Which equation has no solution?

a. 5m-6=5m+7-m
b. 3w+4-w=5w-2(w-2)
c. 7y+9=7y-6
d. 4z+8=-4z-2

Answer 1

C. Because 7y -7y = -15
0 = -15

Answer 2

The equation which has no solution is:

Option: C

c)
`7y+9=7y-6`

Explanation:

The equation is said to have a no solution if we get a false identity on solving the equation.

a)

`5m-6=5m+7-m`

On combining the like terms in the right hand side of the equation we have:

`5m-6=5m-m+7\\\\5m-6=4m+7\\\\5m-4m=7+6\\\\m=13`

Hence, we get a unique solution to the equation.

b)

`3w+4-w=5w-2(2w-2)`

on using the distributive property in the right hand side of the equation we have:

`3w+4-w=5w-2* w-2* (-2)\\\\3w-w+4=5w-2w+4\\\\2w+4=3w+4\\\\3w-2w=4-4\\\\w=0`

Again we get a unique solution to the equation.

c)

`7y+9=7y-6`

on subtracting 7y from both the sides of the equation we have:

`7y-7y-6=9\\\\-6=9`

which is a false identity.

Hence, the equation has no solution.

d)

`4z+8=-4z-2\\\\i.e.\\\\4z+4z=-2-8\\\\8z=-10\\\\z=(-10)/(8)\\\\z=(-5)/(4)`

This equation has a unique solution.