Find all xx with 6x−1<2x−66x−1<2x−6.

Provide your answer in the form x=ax=a or (x≤a)∨(x≥b)

We are given the inequality:

\[
6x - 1 < 2x - 6
\]

### Step 1: Move all terms involving \( x \) to one side
Subtract \( 2x \) from both sides of the inequality:

\[
6x - 2x - 1 < -6
\]

This simplifies to:

\[
4x - 1 < -6
\]

### Step 2: Isolate the \( x \)-term
Now, add 1 to both sides of the inequality:

\[
4x < -6 + 1
\]

This simplifies to:

\[
4x < -5
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 4:

\[
x < \frac{-5}{4}
\]

### Final Answer:
The solution is:

\[
x < -\frac{5}{4}
\]

In set notation, the solution can be written as:

\[
x \leq -\frac{5}{4}
\]

Let me know if you'd like any further details!

Here are some related questions you might find helpful:
1. What is the solution to \( 5x + 3 \geq 2x - 4 \)?
2. How do you solve the inequality \( 7x - 8 > 3x + 5 \)?
3. Can inequalities be solved the same way as equations?
4. How do you graph the solution to \( x \leq -\frac{5}{4} \) on a number line?
5. What happens if you multiply or divide both sides of an inequality by a negative number?

**Tip:** Remember, when solving inequalities, if you multiply or divide by a negative number, you must reverse the inequality sign!

Find all xx with 6x−1<2x−66x−1<2x−6.

Learn how to solve the inequality 6x - 1 < 2x - 6 step by step. This problem covers key algebraic concepts like solving inequalities, simplifying linear expressions, and applying properties of inequalities. Suitable for students in Grades 8-10.

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