Solve this inequality
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution to the inequality:
Given the inequality:
$$2x - 5 \le 3x + 7$$
Step 1: Subtract $2x$ from both sides of the inequality to gather the $x$ terms on one side.
$$2x - 5 - 2x \le 3x + 7 - 2x$$
$$-5 \le x + 7$$
Step 2: Subtract 7 from both sides of the inequality to isolate $x$.
$$-5 - 7 \le x + 7 - 7$$
$$-12 \le x$$
Step 3: Rewrite the inequality with $x$ on the left side.
$$x \ge -12$$
The solution to the inequality is $\boxed{x \ge -12}$.
