Solving the Inequality -2x – 4 ≤ 2x + 4 Explained
| Mathematical Steps | Plain English Explanation |
|---|---|
| Start with the original inequality: -2x – 4 ≤ 2x + 4 | We begin with the inequality we want to solve. The goal is to find all values of x that make this statement true. |
| Combine like terms: -2x – 2x ≤ 4 + 4 | We move all the terms involving x to one side and the constant terms to the other side. We do this by adding 2x and 4 to both sides. |
| Simplify: -4x ≤ 8 | After combining like terms, we get a simpler inequality -4x ≤ 8. |
| Divide by -4: x ≥ -2 | We divide both sides by -4 to isolate x. Note that when we divide by a negative number, the inequality sign flips. |
| Inequality Form: x ≥ -2 | The inequality form of the solution is x ≥ -2. This means x can be any number greater than or equal to -2. |
| Set Builder Form: {x | x ≥ -2} | In set builder notation, the solution is written as {x | x ≥ -2}, which means the set of all x such that x is greater than or equal to -2. |
| Interval Form: [-2, ∞) | In interval notation, the solution is [-2, ∞). This means x can be any number from -2 to infinity, including -2. |
Final Result
The solution to the inequality -2x – 4 ≤ 2x + 4 is x ≥ -2. In set builder notation, it’s {x | x ≥ -2}, and in interval notation, it’s [-2, ∞).
