Question

solve the inequality and graph the solution.
( t - 3 leq 3 )
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
<---(-10)---(-8)---(-6)---(-4)---(-2)---(0)---(2)---(4)---(6)---(8)---(10)--->
submit

Explanation:

Step1: Add 3 to both sides

To solve the inequality \( t - 3 \leq 3 \), we add 3 to both sides of the inequality. This is done to isolate the variable \( t \). The operation is \( (t - 3) + 3 \leq 3 + 3 \).

Step2: Simplify both sides

Simplifying the left side, \( (t - 3) + 3 \) simplifies to \( t \). Simplifying the right side, \( 3 + 3 = 6 \). So we get \( t \leq 6 \).

Answer:

The solution to the inequality \( t - 3 \leq 3 \) is \( t \leq 6 \). To graph this, we draw a number line, mark a closed circle at 6 (since the inequality is "less than or equal to"), and draw an arrow to the left to represent all numbers less than or equal to 6.