Question

solve the inequality and graph the solution.
$f - 5 > 2$
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.

Explanation:

Step1: Add 5 to both sides

To solve the inequality \( f - 5 > 2 \), we add 5 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 inequality sign remains the same.

$$ f - 5 + 5 > 2 + 5 $$

Step2: Simplify both sides

Simplifying the left - hand side, \( f-5 + 5=f \), and simplifying the right - hand side, \( 2 + 5 = 7 \). So we get:

$$ f>7 $$

For graphing the solution:

• We draw a number line.
• Since the inequality is \( f>7 \) (not \( f\geq7 \)), we use an open circle at \( f = 7 \) to indicate that 7 is not included in the solution set.
• Then we draw an arrow starting from the open circle at 7 and pointing to the right (towards positive infinity) to represent all the numbers greater than 7.

Answer:

The solution to the inequality \( f - 5>2 \) is \( f > 7 \). For the graph, there is an open circle at 7 on the number line and an arrow pointing to the right from 7.