Simplify the absolute value on the right side of the 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
Step 1: Simplify the absolute value on the right side of the inequality.
$$ -2 - \frac{3}{5}x \leq \left|\frac{1}{3}\right| $$
$$ -2 - \frac{3}{5}x \leq \frac{1}{3} $$
Step 2: Add 2 to both sides of the inequality.
$$ - \frac{3}{5}x \leq \frac{1}{3} + 2 $$
To add the numbers on the right side, find a common denominator.
$$ - \frac{3}{5}x \leq \frac{1}{3} + \frac{6}{3} $$
$$ - \frac{3}{5}x \leq \frac{7}{3} $$
Step 3: Multiply both sides by $-\frac{5}{3}$ to solve for $x$. Remember to reverse the inequality sign when multiplying or dividing by a negative number.
$$ \left(-\frac{5}{3}\right) \left(-\frac{3}{5}x\right) \geq \left(\frac{7}{3}\right) \left(-\frac{5}{3}\right) $$
$$ x \geq -\frac{35}{9} $$
The solution is:
$$ \boxed{x \geq -\frac{35}{9}} $$
