-|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 will follow these steps:
Step 1: Isolate the absolute value expression.
Add 4 to both sides of the inequality:
-|5x + 3| ≥ 13
Step 2: Remove the absolute value.
Remember that if |a| ≥ b, then a ≥ b or a ≤ -b.
Applying this rule to our inequality, we get two separate inequalities:
1. 5x + 3 ≥ 13
2. 5x + 3 ≤ -13
Step 3: Solve each inequality separately.
Solving the first inequality:
5x + 3 ≥ 13
Subtract 3 from both sides:
5x ≥ 10
Divide by 5 (since the coefficient of x is 5):
x ≥ 2
Solving the second inequality:
5x + 3 ≤ -13
Subtract 3 from both sides:
5x ≤ -16
Divide by 5:
x ≤ -16/5 (or -3.2)
Thus, the solution to the inequality -|5x + 3| - 4 ≥ 9 is x ≥ 2 or x ≤ -16/5 (or x ≤ -3.2).