To solve an inequality, we use the same strategy as if it was an equation, applying inverse operations to isolate the variable. Let's look at our given inequality.
f- 6≥-3
To solve this we would add 6 on both sides to isolate the variable.
Extra
Why It Works?
Let's focus on why we could add 6 to both sides of the inequality, and the answer is correct. First, we will recall the Addition Property of Inequality.
Addition Property of Inequality
Adding the same number to both sides of an inequality creates an equivalent inequality. This equivalent inequality will have the same solution as the original inequality.
To better understand this, we will graph this property on a number line. As an example we will use the inequality given in the exercise, f-6 ≥ -3. Let's begin by drawing the inequality on number line.
Now, we will add 6 to both sides of the inequality. This is the same as moving both points 6 units to the right on the number line.
We see that the solutions of the inequality f≥ 3 are all real numbers greater or equal to 3. These are also the solutions to our original inequality f-6 ≥ -3 because of the Addition Property of Inequality.
