Question #04136

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Answer 1 · 2017-07-04T19:05:54

Initial inequality $\to 120 \leq x \leq 180$ $->120<=x<=180$

Additional weight $\to 0 \leq x \leq 60$ $->0<=x<=60$

Let $x$ $x$ be the weight lifted.

Starting point is $120^{lb}$ $120^("lb")$ inclusive giving:

$120^{lb} \leq x$ $120^("lb")<=x$

End point is $180^{lb}$ $180^("lb")$ inclusive giving:

$120 \leq x \leq 180$ $120<=x<=180$

Subtract 120 from both limiting values

$(120 - 120) \leq x \leq (180 - 120)$ $(120-120)<=x<=(180-120)$

$0 \leq x \leq 60$ $0<=x<=60$

Answer 2 · 2017-07-04T19:09:16

$60$ $60$ pounds or less

Ben can lift a maximum of $180$ $180$ pounds.

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

$Rightarrow underline(" " " " " " " " ") le 180$

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.