Open Middle®
Directions: Create an inequality that has no solution.
Hint
What makes an equation have no solution?
How can you write an inequality with no solution?
Answer
There are infinitely many answers. One possible answer is
x < x – 1
Source: Kara Colley
5x > 5x
Could you also have a constraint on what x can be? ex. 1/x > x {for all x >0} is an inequality with no solution. Meaning there ARE solutions, but they are not part of the allowed domain for x.
23x = 23a 2/3
For each a in [0, +infinity), each b in (–infinity, 0], each c in (0, +infinity), each d in (–infinity, 0) and each e,f in R the following inequalities do not have any solution:
x > x + a
x < x – a
x x – b
x >= x + c
x <= x – c
x = x – d
e * x/0 p*x + p*a (multiplying the inequality by p)
x + q > x + q – a (adding q to both sides of the inequality)
x x (rearranging the equation)
Some lines got messed up or disappeared for some reason when submitting the comment. So here are the corrected lines:
x x – b
x = x – d
e * x/0 p*x + p*a (multiplying the inequality by p)
x + q > x + q – a (adding q to both sides of the inequality)
x x (rearranging the equation)”
Wow… I don’t know why it keeps doing that. I’ll try using words instead of symbols then:
x is greater than x minus b
x is less than or equal to x plus d
x is greater than or equal to x minus d.
e times x over 0 is less/greater than f
And neither do any inequalities that are equivalent to these, like for example all inequalities with p, q in R of the form:
p times x is greater than p times x plus p times a (multiplying the inequality by p)
x plus q is greater than x plus q minus a (adding q to both sides of the inequality)
x is less than x plus b (changing the order of addends or factors)
x plus b is greater than x (rearranging the equation)