Question

which number line shows the solutions of $\frac{1}{3} x - 8 \geqslant x + 6$

Answer 1

we have the inequality

1/3x -8 >=x+6

solve for x

Multiply by 3 both sides

x-24 >=3x+18

-24-18 >=3x-x

-42 >=2x

divide by 2 both sides

-21 >=x

Rewrite

x <= -21

so

the solution is the interval (-infinite, -21}

In a number line the solution is the shaded area at left of the number -21 (close circle)

therefore

the solution in the attached figure