Solve 3x≥ 12. Make sure to write your inequality so that x comes first. Note: You will find the option to add a>, , ≥ , or ≤ symbol in the Comparison () keyboard.
The Correct Answer and Explanation is :
The correct answer is: x≥4
To solve the inequality (3x \geq 12) and express it in the form where (x) comes first, we need to isolate (x).
Step 1: Isolate (x)
Start with the original inequality:
[
3x \geq 12
]
To isolate (x), divide both sides by 3. Remember that dividing or multiplying both sides of an inequality by a positive number does not change the direction of the inequality:
[
x \geq \frac{12}{3}
]
Step 2: Simplify
Now, simplify the right side:
[
x \geq 4
]
Final Form
The inequality is now written with (x) coming first:
[
x \geq 4
]
Explanation
An inequality expresses the relationship between two values where one is not necessarily equal to or greater than the other. In this case, (3x \geq 12) means that three times a value (x) is at least 12. The goal is to determine the values of (x) that satisfy this condition.
By dividing both sides of the inequality by 3, we maintained the relationship between the two sides. This step is crucial because it helps to find the boundary or threshold value, which in this case is 4. The inequality (x \geq 4) indicates that (x) can be any number that is 4 or greater. This includes integers (4, 5, 6, …), fractions (4.1, 4.5, etc.), and even infinitely large numbers.
Understanding how to manipulate inequalities is essential in various fields, including mathematics, science, and economics, as it allows for the analysis of conditions that meet certain criteria. In real-life applications, this might represent constraints such as minimum production levels, budget thresholds, or safety requirements. The solution indicates a set of possible values that fulfill the requirement specified by the original inequality.