w-2+3+4x greater than or equal to 2x+6-6x

The inequality is:

\[
w - 2 + 3 + 4x \geq 2x + 6 - 6x
\]

Let's simplify both sides of the inequality.

### Left-hand side:
\[
w - 2 + 3 + 4x = w + 4x + 1
\]

### Right-hand side:
\[
2x + 6 - 6x = -4x + 6
\]

Now the inequality becomes:

\[
w + 4x + 1 \geq -4x + 6
\]

### Step 1: Combine like terms by moving all terms involving \(x\) to one side and constants to the other.

Subtract \(4x\) from both sides:

\[
w + 1 \geq -8x + 6
\]

### Step 2: Subtract 1 from both sides:

\[
w \geq -8x + 5
\]

Thus, the solution to the inequality is:

\[
w \geq -8x + 5
\]

This shows that for any value of \(x\), \(w\) must be greater than or equal to \(-8x + 5\).

Do you want more details or have any questions?

Here are 5 related questions:
1. How do we solve inequalities with multiple variables?
2. Can inequalities be graphed, and how would this one look?
3. What happens if we change the inequality sign to a strict inequality (greater than)?
4. How do we handle inequalities involving absolute values?
5. What strategies exist for solving quadratic inequalities?

**Tip:** When solving inequalities, treat them like equations, but be careful when multiplying or dividing by negative numbers; the inequality sign flips!

Discover how to solve the inequality w-2+3+4x ≥ 2x+6-6x step by step. This solution explains key algebraic concepts like simplification, combining like terms, and solving inequalities. Ideal for students in Grades 8-10.

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