Question #04136

2 Answers
Jul 4, 2017

Initial inequality #->120<=x<=180#

Additional weight #->0<=x<=60#

Explanation:

Let #x# be the weight lifted.

Starting point is #120^("lb")# inclusive giving:

#120^("lb")<=x#

End point is #180^("lb")# inclusive giving:

#120<=x<=180#

Subtract 120 from both limiting values

#(120-120)<=x<=(180-120)#

#0<=x<=60#

Jul 4, 2017

#60# pounds or less

Explanation:

Ben can lift a maximum of #180# pounds.

So the inequality will contain a "less than or equal to" sign before #180#:

#Rightarrow underline(" " " " " " " " ") le 180#

At the moment, Ben is lifting #120# pounds, but he can lift additional weight.

Let's represent this "additional weight" using #x#:

#Rightarrow 120 + x le 180#

Subtracting #120# from both sides of the inequality:

#Rightarrow 120 + x - 120 le 180 - 120#

#Rightarrow x le 60#

#x# is "less than or equal to" #60#, i.e. Ben can lift an additional weight of #60# pounds or less.