Question

10. Han is solving an equation. He took steps that are acceptable but ended up with

equations that are clearly not true.
5x + 6 = 7x + 5 - 2x original equation
5x + 6 = 7x - 2x + 5 apply the commutative property
5x + 6 = 5x+5
combine like terms
6 = 5
subtract 5x from each side
What can Han conclude as
result of these acceptable steps?
A. There's no value of x that can make the equation 5x + 6 = 7x + 5 – 2x true.
B. Any value of x can make the equation 5x + 6 = 7x + 5 - 2x true.
C. x = 6 is a solution to the equation 5x + 6 = 7x + 5 – 2x.
D. x = 5 is a solution to the equation 5x + 6 = 7x + 5 – 2x.

Answer 1

There's no value of x that can make the

equation 5x + 6 = 7x + 5 – 2x true.

Hence, option 'A' is true.

Explanation:

5x + 6 = 7x + 5 - 2x

5x + 6 = 7x - 2x + 5

5x + 6 = 5x+5

substract 5x from each side

5x-5x+6=5x+5-5x

6 = 5

This conclude that the sides of the equation are not equal.

i.e. L.H.S ≠ R.H.S

We know that when L.H.S ≠ R.H.S, then there is no solution of that equation as no x value can satisfy the equation.

Therefore, there's no value of x that can make the equation 5x + 6 = 7x + 5 – 2x true.

Hence, option 'A' is true.