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When solving inequalities, one of the first steps is to isolate the variable. This means getting the variable by itself on one side of the inequality while keeping the equation balanced.
To achieve this, you can add, subtract, multiply, or divide both sides of the inequality by the same number. For instance, in the given exercise, you need to get rid of the -4 that is subtracted from \( \frac{x}{3} \).
You do this by adding 4 to both sides. Here’s how it looks:

• \( \frac{x}{3} - 4 + 4 \leq 1 + 4 \)

Simplifying the inequality step by step keeps it true and unchanged in value.
After simplification, you get:

• \( \frac{x}{3} \leq 5 \)

Now that you’ve isolated the variable term, the next step is to eliminate the fraction (or denominator) present in this term.

Understanding inequality principles is key to solving such problems. Inequalities differ from equations because they show a range of possible solutions rather than a single solution.
The basic principles of inequalities are:

• If you add or subtract the same number from both sides, the inequality remains true.
• Multiplying or dividing both sides of an inequality by a positive number keeps it balanced; the inequality sign does not change.
• Multiplying or dividing by a negative number reverses the inequality sign (e.g., \ \( \leq \ becomes \ > \).

Using these principles, you can break down and solve inequalities step by step while ensuring the inequality itself stays valid.
In the given exercise, adding 4 to both sides and then multiplying both sides by 3 (as 3 is a positive number) helps isolate and simplify the inequality to achieve the final solution.

The multiplication principle helps you clear out fractions by multiplying both sides of the inequality by the denominator.
By doing so, it simplifies the equation, making it easier to isolate the variable. In our example:

• â—¦ \( \frac{x}{3} \leq 5 \)

To eliminate the denominator (3), you multiply both sides by 3:

• \( 3 \cdot \frac{x}{3} \leq 3 \cdot 5 \)

This simplifies to:

• \( x \leq 15 \)

Remember that when multiplying both sides by a positive number, the inequality sign remains unchanged. This step yields a simpler, more straightforward inequality, providing the solution with less complexity.
Always check your work at the end to verify the inequality holds true throughout each step of the process.