The partners are given the literal inequality ax+b>c to solve for x. Joaquin says that he will solve it just like an equation. Serena says that he needs to be careful because if a is a negative number, the solution will be different. What do you say? What are the solutions for the inequality?

Answer 1

a x + b > c

Subtract b to both sides

a x + b - b > c - b

a x > c - b

If you multiply or divide both sides of an inequality by a negative number, reverse the direction of the inequality sign.

So if a > 0 then:

a x > c - b

If a < 0 then:

a x < c - b

Answer 2

Thank you, I appreciate the help!

Answer 3

a > 0

x > ( c - b ) / a

a < 0

x < ( c - b ) / a

Answer 4

ax > c - b
x > (c-b)/a

let's set some values for a, b, c, and x
of course our values have to satisfy the original
eg. x = 3, a = 5 , c = 10, b = 8
in original: 5(3) > 10-8 , true
in my statement: 3 > 2/5 , true

e.g. x = -5, a = 2, b = 20, c = 5
in original: 2(-5) + 20 > 5 , true
in mine: -5 > (5-20)/2 , -5 > -7.5 , true

x=-5 , a= -2, b= -20 c = -5
in original: -2(-5) - 20 > -5 , -10 > -5 , false
in mine: -5 > (-5+20)/-2 , -5 > 7.5 , still false

e.g. x = -5, a=2, b=20,c=-5
original: 2(-5) + 20 > -5 , true
mine: -5 > (-5-20)/2 , -5 > -7.5 , still true

what do you think ?