Question

solve the inequality and graph the solution.
r + 1 < 9
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.
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Explanation:

Step1: Isolate the variable \( r \)

To solve \( r + 1 < 9 \), subtract 1 from both sides of the inequality. This is based on the subtraction property of inequalities, which states that if \( a < b \), then \( a - c < b - c \) for any real number \( c \).

$$ r + 1 - 1 < 9 - 1 $$

Simplifying both sides, we get:

$$ r < 8 $$

Step2: Graph the solution

The solution \( r < 8 \) means all real numbers less than 8. On the number line, we plot an open circle at 8 (because 8 is not included in the solution, as the inequality is strict, \( < \) not \( \leq \)) and draw an arrow to the left (indicating all numbers less than 8).

Answer:

The solution to the inequality \( r + 1 < 9 \) is \( r < 8 \). For the graph, plot an open endpoint at 8 and draw an arrow to the left.