Question

solve for f.
f - 20 ≤ 100
write the solution as an inequality (for example, f > 9).
graph the solution.
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
75 80 85 90 95 100 105 110 115 120 125
submit

Explanation:

Step1: Isolate the variable \( f \)

To solve the inequality \( f - 20 \leq 100 \), we add 20 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same.

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Step2: Graph the solution

• The inequality \( f \leq 120 \) means that \( f \) can take any value less than or equal to 120.
• For the number line:
• Plot a closed dot (because the inequality is "less than or equal to", so 120 is included in the solution set) at 120.
• Draw a ray starting from 120 and extending to the left (towards decreasing values of \( f \)) to represent all values of \( f \) that satisfy the inequality.

Answer:

The solution to the inequality \( f - 20 \leq 100 \) is \( f \leq 120 \). For the graph, plot a closed endpoint at 120 on the number line and draw a ray pointing to the left (towards numbers less than 120).