Question

graph the inequality and check the solution. waseme swam more than 100 laps. ( l > 100 ) check all that apply (square) draw a closed circle at 100. (square) draw an open circle at 100. (square) shade all numbers to the right of 100. (square) shade all numbers to the left of 100. (square) 150 is shaded, so substitute 150 in for the variable to check the graph of the solution. (square) 50 is shaded, so substitute 50 in for the variable to check the graph of the solution.

Explanation:

Step1: Analyze the inequality \( l > 100 \)

For the inequality \( l > 100 \), since the inequality is strict (does not include equality), we use an open circle at 100. This is because 100 is not included in the solution set.

Step2: Determine the shading direction

For \( l > 100 \), the values of \( l \) that satisfy the inequality are greater than 100. On a number line, greater values are to the right of a given number. So we shade to the right of 100.

Step3: Check the substitution

To check the solution, we can substitute a value that is in the shaded region (to the right of 100) into the inequality. 150 is to the right of 100 (in the shaded region), so substituting \( l = 150 \) into \( l > 100 \) gives \( 150 > 100 \), which is true. 50 is to the left of 100 (not in the shaded region), and substituting \( l = 50 \) gives \( 50 > 100 \), which is false, so we do not use 50 for checking.

Answer:

• Draw an open circle at 100.
• Shade all numbers to the right of 100.
• 150 is shaded, so substitute 150 in for the variable to check the graph of the solution.