. The interval representing the solution of the inequality 3𝑥 − 1 ≥ 5, 𝑥 ∈ 𝑅 is

To find the interval representing the solution of the inequality \(3x - 1 \geq 5\), follow these steps:

### Step 1: Solve the inequality
Start by isolating the variable \(x\):

\[
3x - 1 \geq 5
\]

Add 1 to both sides:

\[
3x \geq 6
\]

Next, divide both sides by 3:

\[
x \geq 2
\]

### Step 2: Express the solution as an interval
The inequality \(x \geq 2\) means that \(x\) can be any real number greater than or equal to 2.

This is expressed in interval notation as:

\[
[2, \infty)
\]

### Final Answer:
The interval representing the solution is \([2, \infty)\).

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Would you like any more details or have any questions? Here are some related questions for further practice:

1. Solve and express the interval for the inequality \(2x + 3 < 7\).
2. Solve and express the interval for the inequality \(4x - 8 \leq 12\).
3. Solve and express the interval for the inequality \(5x + 9 > 14\).
4. Solve and express the interval for the inequality \(6x - 2 \geq 10\).
5. Solve and express the interval for the inequality \(x^2 - 4x + 4 \leq 0\).

**Tip:** When writing intervals, remember that brackets \([ \text{ and } ]\) are used for "greater than or equal to" (≥) or "less than or equal to" (≤), while parentheses \(( \text{ and } )\) are used for strict inequalities (greater than or less than).

Learn how to find the interval solution for the inequality 3x - 1 ≥ 5 step-by-step. This problem covers inequalities and interval notation. Suitable for students in Grades 7-9.

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