How to Solve One-Step Inequalities | Math with Mr. J

Solving One-Step Inequalities
📌 To solve one-step inequalities, the goal is to isolate the variable using the inverse operation, keeping the equation balanced by applying the operation to both sides.
📌 Unlike equations, one-step inequalities result in an infinite amount of solutions.
📌 A critical rule is to flip the inequality symbol when multiplying or dividing both sides by a negative number.

Example Walkthroughs and Verification
✅ Example 1: $y + 7 < 8$ simplifies to $y < 1$. Testing $y=0$ confirms the solution since $0 + 7 < 8$ (i.e., $7 < 8$) is true.
✅ Example 2: $\frac{x}{5} \ge 3$ requires multiplying by 5, resulting in $x \ge 15$. Testing $x=20$ is valid since $\frac{20}{5} = 4$, and $4 \ge 3$.
✅ Example 3: $14 \ge n - 11$ involves adding 11 to both sides, yielding $25 \ge n$, or $n \le 25$.
✅ Example 4 involves dividing by a negative number: $-6r < 36$ requires division by $-6$, necessitating flipping the symbol to get $r > -6$.

Key Points & Insights
➡️ Isolate the variable by using the inverse operation while maintaining balance across both sides of the inequality.
➡️ Remember the crucial step: flip the inequality symbol if you multiply or divide both sides by a negative value.
➡️ Solutions for one-step inequalities represent a range of numbers (infinite solutions), not a single value like in equations.

📸 Video summarized with SummaryTube.com on Feb 02, 2026, 09:34 UTC