How would this inequality be solved?
|7d| > -43
There is no reference to this type of problem in the textbook.
Thanks
when d is positive, where is 7 d >-43
well whenever d >-43/7
when d is negative, when is |d|>-43
well whenever d < -43/7
in other words for all real d
IN FACT:
the absolute value of any old number is positive.
It is greater than ANY negative number
To solve the given inequality: |7d| > -43, we can follow these steps:
Step 1: Remove the absolute value symbol by considering two cases:
Case 1: 7d > -43
To solve this, we can isolate the variable "d" by dividing both sides of the inequality by 7:
(7d)/7 > (-43)/7
d > -43/7
Note: When dividing an inequality by a positive number, the direction of the inequality remains the same.
Case 2: -(7d) > -43
To solve this, we need to divide both sides of the inequality by -7, but we need to remember that dividing by a negative number flips the inequality direction:
(7d)/(-7) < (-43)/(-7)
d < -43/(-7)
d < 43/7
Step 2: Analyze the solutions from both cases and determine the final solution.
In this case, we end up with two separate solutions for d:
Solution 1: d > -43/7
Solution 2: d < 43/7
Thus, the solution to the given inequality |7d| > -43 is:
d > -43/7 OR d < 43/7