suppose you have an equation in the form of ax+b=2x-5

Question

I. If this has infintiely many solution. What can you say about a and or b? Explain

II. If this has no solutions what can you say about a and or b?Explain

III. if this has exactly one solution what can you say about a and or b? Explain

Answer 1

The questions asked are those normally asked of a quadratic equation, yet the equation is linear.

Are you sure it's the right equation?

===== 4/10/14

Comments jogged my memory (thanks guys), so here's a revised answer.

Suppose you have an equation in the form of ax+b=2x-5

I. If this has infinitely many solutions, what can you say about a and or b? Explain.

To have infinitely many solutions the equation should evaluate to a true statement without regard to the value for x.

To do that a = 2 and b = -5: 2x-5=2x-5 ==> 0 = 0, which is true for any x.

II. If this has no solutions what can you say about a and or b? Explain.

To have no solutions the equation should evaluate to a false statement without regard to the value for x.

To do that a = 2 and b ≠ -5: 2x+9=2x-5 ==> 9 = -5, which is false for any x.

III. If this has exactly one solution what can you say about a and or b? Explain.

To have one solution the equation should evaluate to x = (a number).

To do that a ≠ 2 and b is any real number: 3x+9=2x-5 ==> x = -14.

Answer 2

(a-2)x=-b-5.

 

I a=2, b=-5. Since 0 * x=0, x can be any number.

 

II a=2, b≠-5, since 0*x≠0 has no solution.

 

III a≠2, x=(-b-5)/(a-2).