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

Explanation:

Step1: Analyze the first inequality

The inequality $x < 5$ represents all real - numbers less than 5. On a number line, we use an open circle at 5 and draw an arrow to the left.

Step2: Analyze the second inequality

The inequality $x < 6$ represents all real - numbers less than 6. On a number line, we use an open circle at 6 and draw an arrow to the left.

Step3: Determine the solution set for the 'or' compound inequality

For an 'or' compound inequality, the solution set is the union of the solution sets of the individual inequalities. Since all numbers that satisfy $x < 5$ also satisfy $x < 6$, the solution set of $x < 5$ or $x < 6$ is $x < 6$. On a number line for the solution set, we use an open circle at 6 and draw an arrow to the left.

Answer:

The solution of the compound inequality is $x < 6$. For the first number line (for $x < 5$): Open circle at 5, arrow to the left. For the second number line (for $x < 6$): Open circle at 6, arrow to the left. For the third number line (for the solution set): Open circle at 6, arrow to the left.