Logan Mccarthy
05/02/2023 · Elementary School
Solve the compound inequality. Graph the two inequalities on the frirst wo number lines and the solution set on the third number line. Write the solution in interval notation. \( x<1 \) and \( x>-2 \)
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Step-by-step Solution
Solve the equation \( x<1 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(x<1\)
Solve the equation \( x>-2 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(x>-2\)
The solution to the compound inequality \( x<1 \) and \( x>-2 \) is \( x<-2 \) and \( x<1 \).
To graph the two inequalities on the first two number lines, we have:
- For \( x<1 \), the graph is a line below 1.
- For \( x>-2 \), the graph is a line above -2.
The solution set on the third number line is the intersection of the two graphs, which is the region between -2 and 1, excluding -2 and 1.
In interval notation, the solution is \((-2, 1)\).
Quick Answer
The solution in interval notation is \((-2, 1)\).
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