How is (x\le 5) represented on the number line?

Correct answer: closed dot at (5) and shading to the left

The correct answer is option A: a closed dot at 5 with shading to the left. The inequality \(x\le5\) means x can be 5 or any number smaller than 5. Because equality is allowed, the point 5 must be included, so we draw a filled or closed dot. Smaller numbers lie to the left on a horizontal number line, so shade leftward. Option A shows both required features. Option B uses an open dot, which would mean 5 is excluded, as in \(x<5\). Option C uses a closed dot correctly for inclusion but shades right, representing numbers greater than or equal to 5. Option D uses an open dot and shades right, representing \(x>5\). Thus only A matches the inequality. Memory cue: filled means included; left means less than. The symbol \(\le\) combines both ideas.