Solve the inequality:
Absolute Value of X+5 is greater than or equal to 1.
I'd appreciate someone telling me how to solve it and get the answer. Thank you
[x+5]> 1
-
x+5>1
You subtract 1 from both sides
ok thanks
To solve the inequality |x+5| ≥ 1, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: (x+5) ≥ 1
In this case, we remove the absolute value and solve for x:
x+5 ≥ 1
Subtract 5 from both sides of the inequality:
x ≥ 1 - 5
x ≥ -4
Case 2: -(x+5) ≥ 1
In this case, we need to change the sign of the inequality when we remove the absolute value:
x+5 ≤ -1
Subtract 5 from both sides of the inequality:
x ≤ -1 - 5
x ≤ -6
So, the solutions to the inequality are x ≥ -4 or x ≤ -6. We can represent this on a number line by shading the regions below -6 and above -4. The shaded regions indicate all the values of x that satisfy the inequality.