To solve the inequality using a sign chart, we need to consider the intervals where each expression on either side of the inequality sign is positive or negative.
Starting with the expression x - 5, we can determine when it is positive or negative by examining the factors that make it zero:
x - 5 = 0
x = 5
This means that the expression x - 5 changes sign at x = 5.
Next, let's consider the expression -11x - 6. To determine its sign, let's set it equal to zero:
-11x - 6 = 0
-11x = 6
x = -6/11
This means that the expression -11x - 6 changes sign at x = -6/11.
Now let's create a sign chart:
Interval | x - 5 | -11x - 6 | x - 5 >= -11x - 6
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x < -6/11 | - | + | Yes
-6/11 < x < 5 | - | - | No
x > 5 | + | - | Yes
From the sign chart, we can see that the inequality x - 5 >= -11x - 6 is satisfied when x < -6/11 or x > 5.
solve inequality with sign chart:
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