Multiply the entire inequality by the least common multiple of the denominators (2 and 3), which is 6, to eliminate the fractions.
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
You're on a roll — here is the solution for the inequality:
$$\frac{1}{2}(x-1) - \frac{1}{3}(x+5) \le 1$$
Step 1: Multiply the entire inequality by the least common multiple of the denominators (2 and 3), which is 6, to eliminate the fractions.
$$6 \times \frac{1}{2}(x-1) - 6 \times \frac{1}{3}(x+5) \le 6 \times 1$$
$$3(x-1) - 2(x+5) \le 6$$
Step 2: Distribute the 3 and the $-2$ into their respective parentheses.
$$3x - 3 - 2x - 10 \le 6$$
Step 3: Combine like terms on the left side.
$$(3x - 2x) + (-3 - 10) \le 6$$
$$x - 13 \le 6$$
Step 4: Add 13 to both sides of the inequality to isolate $x$.
$$x \le 6 + 13$$
$$x \le 19$$
The solution is:
$$\boxed{x \le 19}$$
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