Final answer:
To solve the inequalities 3x-5<=-23 or 2x-6>=-6, we isolate x for each to find x<=-6 and x>=0. Graphing these on a number line involves shading left from -6 and right from 0, respectively, with solid dots to indicate the inequality is inclusive.
Step-by-step explanation:
The student's question involves solving two separate inequalities and graphing their solutions on a number line. To find the solutions, we'll need to isolate x in both of the inequalities.
Starting with the first inequality 3x - 5 ≤ -23, we can solve for x by adding 5 to both sides to get 3x ≤ -18, and then dividing by 3 to obtain x ≤ -6.
For the second inequality 2x - 6 ≥ -6, we add 6 to both sides to get 2x ≥ 0, and then divide both sides by 2 resulting in x ≥ 0.
To graph the solutions on a number line, we would draw a solid dot at x = -6 and shade to the left for the first inequality since it includes values less than or equal to -6. For the second inequality, we would draw a solid dot at x = 0 and shade to the right since it includes values greater than or equal to 0. The final graph will show the entire number line shaded because the inequalities are joined by an 'or', meaning any number that satisfies either inequality is part of the solution set.