|x-4|-6 answer:x=10,-2
i need help on this one please:
|5x+3|-4 is greater than or equal to 9
To solve the inequality |5x+3|-4 >= 9, we can follow these steps:
Step 1: Remove the absolute value brackets by considering two cases, one with a positive expression inside the brackets, and one with a negative expression inside the brackets.
For the positive case, we have:
5x + 3 - 4 >= 9
Simplifying this inequality, we have:
5x - 1 >= 9
Step 2: Solve the inequality for the positive case:
5x >= 9 + 1
5x >= 10
Divide both sides of the inequality by 5:
x >= 2
For the negative case, we have:
-(5x + 3) - 4 >= 9
Simplifying this inequality, we have:
-5x - 7 >= 9
Step 3: Solve the inequality for the negative case:
-5x >= 9 + 7
-5x >= 16
Divide both sides of the inequality by -5 (remember to flip the inequality sign when dividing by a negative number):
x <= -16/5
Step 4: Combine the solutions from the positive and negative cases to find the final solution:
The solution to the inequality |5x+3|-4 >= 9 is:
x >= 2 or x <= -16/5
Therefore, the solution set for the inequality is x >= 2 or x <= -16/5.