Question

Bradley wrote the beginning of an equation, 3··8x 1 12 5 u. Part A Finish the equation so that the equation will have no solution. Explain how you know.

Answer 1

Question:

Bradley wrote the beginning of an equation,
`(3)/(8)x + 12 =`

Finish the equation so that the equation will have no solution. Explain how you know.

Answer:

`(3)/(8)x + 12 =(3)/(8)x -4`

Explanation:

Given

`(3)/(8)x + 12 =`

Required

Complete the equation to have no solution

The given equation is a linear equation in form of
`mx + b`

Where
`m = (3)/(8)`

Compare both equations

`(3)/(8)x + 12 = mx + b`

Substitute
`(3)/(8)` for m

`(3)/(8)x + 12 = (3)/(8)x + b`

Collect Like Terms

`b = (3)/(8)x - (3)/(8)x + 12`

`b = 12`

This implies that, for the equation to have a solution the value of b must be 12.

However, for the equation not to have a solution, the value of b must not equal 12

i.e.

`b \\e 12`

This implies that, we can assume any value, other than 12 for b so that the equation will not have a solution.

Say for instance: b = -4

`(3)/(8)x + 12 = mx + b`

Substitute -4 for b and 3/8x for m. This gives:

`(3)/(8)x + 12 =(3)/(8)x -4`