Question

solve the compound inequality. graph the two inequalities on the first two number - lines and the solution set on the third number line.
x<5 or x<6
graph the inequality x<5. choose the correct graph below
graph the inequality x<6. choose the correct graph below.
graph the solution set on the number line. choose the correct graph below.

Explanation:

Step1: Graph \(x < 5\)

The inequality \(x<5\) represents all real - numbers less than 5. On a number line, we use an open circle at 5 (because 5 is not included in the solution set) and draw an arrow to the left. So the correct graph for \(x < 5\) is the one with an open circle at 5 and an arrow pointing left.

Step2: Graph \(x < 6\)

The inequality \(x<6\) represents all real - numbers less than 6. On a number line, we use an open circle at 6 (since 6 is not included in the solution set) and draw an arrow to the left.

Step3: Analyze the compound inequality \(x < 5\) or \(x < 6\)

The solution set of \(x < 5\) or \(x < 6\) is the set of all real numbers less than 6. Because if a number is less than 5, it is also less than 6. So the solution set of the compound inequality is the set of all real numbers \(x\) such that \(x<6\). On a number line, we use an open circle at 6 and draw an arrow to the left.

Answer:

For \(x < 5\): The correct graph is the one with an open - circle at 5 and an arrow pointing left.
For \(x < 6\): The correct graph is the one with an open - circle at 6 and an arrow pointing left.
For the solution set of \(x < 5\) or \(x < 6\): The correct graph is the one with an open - circle at 6 and an arrow pointing left.