Question

solve for x and choose the correct solution: $x - 3 leq - 2$ $x leq - 5$ $x leq 1$ $x leq - 5$ $x leq 1$

Explanation:

Step1: Solve the inequality

Add \(3\) to both sides of \(x - 3\leq - 2\).
$$x-3 + 3\leq - 2+3$$
$$x\leq1$$

Step2: Analyze the number - line representation

For the inequality \(x\leq a\), if the circle on the number - line is filled, it means \(a\) is included in the solution set. Here \(a = 1\), and the correct number - line should have a filled circle at \(1\) and the arrow pointing to the left (since \(x\) is less than or equal to \(1\)).

Answer:

The second option \(x\leq1\) with the filled - circle number - line (the last option in the given choices where \(x\leq1\) has a filled circle at \(1\)) is correct.