Final answer:
To solve the linear inequality, distribute and simplify the expression, isolate the variable x, and represent the solution set on a number line.
Step-by-step explanation:
To solve the linear inequality, 2(5-x) ≤ 3(5-x) - 7x, we first distribute the numbers on the right side of the inequality sign: 10 - 2x ≤ 15 - 3x - 7x. Simplifying this expression gives us 10 - 2x ≤ 15 - 10x. Next, we can simplify the expression further by combining like terms: 10 + 15 ≤ 15x - 2x - 10x. This gives us 25 ≤ 3x. The next step is to isolate the variable x by dividing both sides of the inequality by 3: 25/3 ≤ x. We can represent this solution set on a number line by shading the area to the right of 25/3.