Question
Solve and graph the compound inequality on a number line.
x4 < −1 and x + 6 > −2
(1 point)
x4 < −1 and x + 6 > −2
(1 point)
Answers
GPT 3.5
To solve the compound inequality, we'll solve each inequality separately and then consider the overlap between the two solutions.
First, let's solve the first inequality:
x + 4 < -1
Subtracting 4 from both sides, we get:
x < -1 - 4
x < -5
Next, let's solve the second inequality:
x + 6 > -2
Subtracting 6 from both sides, we get:
x > -2 - 6
x > -8
Now, let's consider the overlap between the two solutions:
For x < -5 and x > -8, the only values that satisfy both inequalities are x > -5 and x > -8.
Graphing this on a number line, we'll shade the region to the right of -5 and -8 (as we need x to be greater than both):
-------------(=|----------------------------|===>
-8 -5
In interval notation, the solution is:
(-5, ∞)
First, let's solve the first inequality:
x + 4 < -1
Subtracting 4 from both sides, we get:
x < -1 - 4
x < -5
Next, let's solve the second inequality:
x + 6 > -2
Subtracting 6 from both sides, we get:
x > -2 - 6
x > -8
Now, let's consider the overlap between the two solutions:
For x < -5 and x > -8, the only values that satisfy both inequalities are x > -5 and x > -8.
Graphing this on a number line, we'll shade the region to the right of -5 and -8 (as we need x to be greater than both):
-------------(=|----------------------------|===>
-8 -5
In interval notation, the solution is:
(-5, ∞)