Question

Can someone please help me find the value of w?

Answer 1

Answer

Full solution is 17.6 ≤ w ≤ 18.4

For the interpretation, the actual weight of the corn flakes vary from 17.6 oz. to 18.4 oz. inclusive.

The graph of this solution is attached below

Explanation

To solve an expression with the absolute value symbol, we obtain two solutions for it.

We first solve when the other side of the equation to the absolute value symbol has positive sign.

Then, we obtain another solution by setting that other side (the right-hand side) to negative. For equations involving inequality signs, the second solution usually changes the inequality sign.

We are asked to solve the inequality

|w - 18| ≤ 0.4

First solution,

w - 18 ≤ 0.4

Add 18 to both sides

w - 18 + 18 ≤ 0.4 + 18

w ≤ 18.4

Second solution,

w - 18 ≥ -0.4

Add 18 to both sides

w - 18 + 18 ≥ -0.4 + 18

w ≥ 17.6

So, we can then write the full solution as

17.6 ≤ w ≤ 18.4

For the interpretation, the actual weight of the corn flakes vary from 17.6 oz. to 18.4 oz. inclusive.

For the graph,

In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.

But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.

For this solution, the two inequality signs are ≤, hence, the the two circles will be shaded, then the region covered will be the space between 17.6 and 18.4 to indicate that it satisfies the condition of w being greater than or equal to 17.6 and less thanor equal to 18.4

The graph willbe uploaded under 'Answer' above.

Hope this Helps!!!