A meteorologist announces that yesterday’s high temperature was within 4° Celsius of 18° Celsius all across the country. Write an inequality that involves an absolute value to represent yesterday’s high temperature. Solve the inequality and explain the meaning of the solution.
|T - 18| </= 4
To represent yesterday's high temperature using an absolute value, we need to find the range of temperatures that are within 4° Celsius of 18° Celsius.
Let's assume x represents the high temperature in Celsius. Since the temperature is within 4° Celsius of 18° Celsius, the inequality can be written as:
| x - 18 | ≤ 4
Now, let's solve this inequality step by step:
1. Remove the absolute value sign:
x - 18 ≤ 4 and x - 18 ≥ -4
2. Solve the first inequality:
x ≤ 4 + 18 → x ≤ 22
3. Solve the second inequality:
x ≥ -4 + 18 → x ≥ 14
The solution to the given inequality is 14 ≤ x ≤ 22.
This means that yesterday's high temperature, represented by x, was between 14°C and 22°C, inclusive. Any temperature within this range satisfies the given condition that it is within 4° Celsius of 18° Celsius.
To represent yesterday's high temperature, we can let the variable "x" represent the temperature. Given that the high temperature was within 4° Celsius of 18° Celsius, the absolute value of the difference between "x" and 18 should be less than or equal to 4.
The inequality can be written as: |x - 18| ≤ 4.
To solve this inequality, we can consider two cases: when x - 18 is positive and when it is negative.
Case 1: x - 18 ≥ 0 (x is greater than or equal to 18)
In this case, the absolute value sign is unnecessary, so we can simplify the inequality to x - 18 ≤ 4. Adding 18 to both sides, we have x ≤ 22.
Case 2: x - 18 < 0 (x is less than 18)
In this case, we need to multiply both sides of the inequality by -1 to remove the negative sign. This gives us -(x - 18) ≤ 4. Simplifying further, -x + 18 ≤ 4. Subtracting 18 from both sides, we have -x ≤ -14. Dividing by -1 (which reverses the inequality), we get x ≥ 14.
Therefore, the solution to the inequality is 14 ≤ x ≤ 22.
This means that yesterday’s high temperature was between 14°C and 22°C, inclusive, in all locations across the country.