# Question #04136

Jul 4, 2017

Initial inequality $\to 120 \le x \le 180$

Additional weight $\to 0 \le x \le 60$

#### Explanation:

Let $x$ be the weight lifted.

Starting point is ${120}^{\text{lb}}$ inclusive giving:

${120}^{\text{lb}} \le x$

End point is ${180}^{\text{lb}}$ inclusive giving:

$120 \le x \le 180$

Subtract 120 from both limiting values

$\left(120 - 120\right) \le x \le \left(180 - 120\right)$

$0 \le x \le 60$

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 $180$:

$R i g h t a r r o w \underline{\text{ " " " " " " " }} \le 180$

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

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

$R i g h t a r r o w 120 + x \le 180$

Subtracting $120$ from both sides of the inequality:

$R i g h t a r r o w 120 + x - 120 \le 180 - 120$

$R i g h t a r r o w x \le 60$

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