If a bag of chips is within .4 oz of 6 oz then it is allowed to go on the market. Write an inequality that models this situation. Solve the inequality.
Sure, here's an inequality that models the situation:
6 - 0.4 ≤ x ≤ 6 + 0.4
To solve the inequality, we simplify it:
5.6 ≤ x ≤ 6.4
Therefore, a bag of chips is allowed to go on the market if it weighs between 5.6 oz and 6.4 oz. Keep in mind that these are approximate values since chips are often measured in ounces to some decimal places.
Let's call the weight of the bag of chips "w" in ounces. According to the given condition, the bag of chips is allowed to go on the market if it is within 0.4 oz of 6 oz.
To represent this situation with an inequality, we can use the absolute value function. The absolute value of the difference between the weight of the bag of chips and 6 oz should be less than or equal to 0.4 oz.
Mathematically, this can be written as:
|w - 6| ≤ 0.4
To solve this inequality, we split it into two cases:
Case 1: w - 6 ≤ 0.4
Solving for w:
w ≤ 6 + 0.4
w ≤ 6.4
Case 2: -(w - 6) ≤ 0.4
Solving for w:
-w + 6 ≤ 0.4
6 - 0.4 ≤ w
5.6 ≤ w
Combining the results from both cases, we have:
5.6 ≤ w ≤ 6.4
Therefore, the bag of chips is allowed to go on the market if its weight is between 5.6 oz and 6.4 oz (inclusive).
To write an inequality that models this situation, let's assign a variable to the weight of the bag of chips. Let's call it "x."
According to the given information, if the weight of the bag of chips is within 0.4 oz of 6 oz, then it is allowed to go on the market.
So, we can express this as:
|x - 6| ≤ 0.4
The inequality represents the absolute value of the difference between the weight of the bag of chips (x) and 6 oz, which should be less than or equal to 0.4 oz.
Now we can solve this inequality:
First, we'll split the inequality into two separate inequalities:
x - 6 ≤ 0.4 and -(x - 6) ≤ 0.4
Simplifying each inequality:
x ≤ 6 + 0.4 and -x + 6 ≤ 0.4
x ≤ 6.4 and -x + 6 ≤ 0.4
To isolate x in the second inequality, we'll subtract 6 from both sides:
-x ≤ 0.4 - 6
This gives us:
-x ≤ -5.6
Next, we'll divide both sides of the inequality by -1. Remember that when you divide an inequality by a negative number, the inequality sign flips:
x ≥ 5.6
Therefore, the solution to the inequality |x - 6| ≤ 0.4 is:
5.6 ≤ x ≤ 6.4