Question

tomas wrote an equation 4/5x-8=. Finish the equation so that the equation will have no solution. Explain how you know.

Answer 1

Right part:
`(4)/(5)x+a,` where
`a\\eq -8.`

Explanation:

Linear equation have no solution if it is impossible for the equation to be true no matter what value we assign to the variable x.

The left part of the equation Tomas wrote is

`(4)/(5)x-8.`

The right part of the equation should be of the form

`(4)/(5)x+a,`

where
`a\\eq -8.`

In this case, the equation will take look

`(4)/(5)x-8=(4)/(5)x+a,\\ \\-8=a.`

Since
`a\\eq -8,` this equality is always false.

Remark: 1) If a=8, the equation
`(4)/(5)x-8=(4)/(5)x+a` is equivalent to the equation

`(4)/(5)x-8=(4)/(5)x-8,\\ \\0=0`

and the lest equation has infinitely many solutions.

2) When coefficient at x differs from
`(4)/(5),` the equation has unique solution.