Question

solve the linear inequality for y and graph the answer in the number line. then write the solution in inequality notation.
y - 2 < 5
show your work here
hint to add inequalities (<, >, ≤, ≥), type \less\ or \greater\
-15 -10 -5 0 5 10 15
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solution:

Explanation:

Step1: Add 2 to both sides

To isolate \( y \), we add 2 to both sides of the inequality \( y - 2 < 5 \). This gives us \( y - 2 + 2 < 5 + 2 \).

Step2: Simplify both sides

Simplifying the left side, \( y - 2 + 2 \) becomes \( y \). Simplifying the right side, \( 5 + 2 \) is \( 7 \). So we have \( y < 7 \).

Answer:

The solution to the inequality \( y - 2 < 5 \) is \( y < 7 \). To graph this on the number line, we would have an open circle at 7 (since the inequality is strict, \( < \), not \( \leq \)) and a line extending to the left from 7 to represent all numbers less than 7.