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.
|x-6| ≤ 0.4
6-0.4 ≤ x ≤ 6+0.4
Let x represent the weight, in ounces, of the bag of chips.
According to the given information, the bag of chips is allowed to go on the market if it is within 0.4 oz of 6 oz. This can be represented by the inequality:
|x - 6| ≤ 0.4
To solve this inequality, we can break it down into two separate inequalities:
1. x - 6 ≤ 0.4
2. -(x - 6) ≤ 0.4
Solving the first inequality:
x - 6 ≤ 0.4
x ≤ 0.4 + 6
x ≤ 6.4
Solving the second inequality:
-(x - 6) ≤ 0.4
-x + 6 ≤ 0.4
-x ≤ 0.4 - 6
-x ≤ -5.6
Multiplying both sides of the second inequality by -1 (which reverses the inequality sign):
x ≥ 5.6
Therefore, the solution to the inequality |x - 6| ≤ 0.4 is 5.6 ≤ x ≤ 6.4.
To write an inequality that models the situation, let's first define a variable.
Let's say x represents the weight of the bag of chips in ounces.
According to the problem, the bag of chips is allowed to go on the market if it is within 0.4 oz of 6 oz. This means that the weight of the bag of chips, x, should satisfy the inequality:
6 oz - 0.4 oz ≤ x ≤ 6 oz + 0.4 oz
Simplify this inequality:
5.6 oz ≤ x ≤ 6.4 oz
Now, to solve this inequality, we need to consider the range of values that x can take. Since the bag of chips must weigh at least 5.6 oz and no more than 6.4 oz, the solution to the inequality is the interval [5.6, 6.4].
Therefore, any bag of chips with a weight in the range of 5.6 to 6.4 ounces (inclusive) is allowed to go on the market.