Question

A company did a quality check on all the packs of nuts it manufactured. Each pack of nuts is targeted to weigh 18.25 oz. A pack must weigh within 0.36 oz of the target weight to be accepted. Find the absolute value inequality that describes the situation and solve it to find the range of rejected masses, x.

 |x − 18.25| > 0.36; x < 17.89 or x > 18.61 |x − 0.36| + 18.25 > 0; x < 17.89 or x > 18.61 |x − 18.25| > 0.36; x < 18.25 or x > 18.61 |x − 0.36| + 18.25 > 0; x < 18.25 or x > 18.61

Answer 1

Answer:

$x < 17.89$ or $x > 18.61$ , since $\left | x-18.25 \right |>0.36$

Step-by-step explanation:

According to the question the weight is rejected if it is more than 0.36 oz, the weight should not be beyond 0.36 oz that is from the target weight of 18.25.  

We can say that, the difference between the actual weight and the target weight is greater than 0.36 oz.

Lets say the actual weight is 'x'. So,

$x-18.25>0.36$

But there can be times when the actual weight 'x' could be less than 0.36, So the order will be changed:

$18.25-x>0.36$

The absolute value will sum up these two into a single inequality:

$|x-18.25|>0.36$

Simplifying the inequalities, we get:

$x-18.25>0.36$

$x>18.61$   (we have added 18.25 on both sides)

 $18.25-x>0.36$

Subtracting 18.25 from both the sides we get:

$-x>-17.89$

After sign change it is:

$x<17.89$

So we can see that only $x < 17.89$ or $x>18.61$ since $\left | x-18.25 \right |>0.36$ is the one that represents the scenario given above.