Final answer:
To solve the inequality 2x ≤ 5x - 15, subtract 5x from both sides, divide by -3, and reverse the inequality sign. The solution is x ≥ 5.
Step-by-step explanation:
To solve the inequality 2x ≤ 5x - 15, we need to isolate the variable x on one side of the equation. We can do this by subtracting 5x from both sides, resulting in -3x ≤ -15. Next, we divide both sides by -3, remembering to reverse the inequality sign since we are dividing by a negative number. This gives us x ≥ 5.
To check our work, we substitute a value greater than or equal to 5 into the original inequality and see if it holds true. For example, if we choose x = 5, the inequality becomes 2(5) ≤ 5(5) - 15, which simplifies to 10 ≤ 25 - 15, and further simplifies to 10 ≤ 10. Since this statement is true, we can conclude that the solution for the inequality is x ≥ 5.
Learn more about Solving inequalities with variable x