Solve for w.
3w–16w–19≥15–15w
Write your answer with w first, followed by an inequality symbol.

Let's solve the inequality \(3w - 16w - 19 \geq 15 - 15w\).

1. **Combine like terms** on the left side:
   \[
   3w - 16w = -13w
   \]
   So the inequality becomes:
   \[
   -13w - 19 \geq 15 - 15w
   \]

2. **Add \(15w\) to both sides** to isolate the terms with \(w\) on one side:
   \[
   -13w + 15w - 19 \geq 15
   \]
   Simplifying this, we get:
   \[
   2w - 19 \geq 15
   \]

3. **Add 19 to both sides** to further isolate \(w\):
   \[
   2w \geq 15 + 19
   \]
   Simplifying further:
   \[
   2w \geq 34
   \]

4. **Divide both sides by 2** to solve for \(w\):
   \[
   w \geq \frac{34}{2}
   \]
   Simplifying the fraction:
   \[
   w \geq 17
   \]

So, the solution is:
\[
w \geq 17
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the solution if the inequality was \(3w - 16w - 19 \leq 15 - 15w\)?
2. How would the solution change if we had \(3w - 16w + 19 \geq 15 - 15w\)?
3. Can you graph the solution \(w \geq 17\) on a number line?
4. What happens if we substitute \(w = 17\) back into the original inequality?
5. How would you solve the inequality \(3w - 16w - 19 > 15 - 15w\)?

**Tip:** Always double-check your solution by substituting it back into the original inequality to ensure it satisfies the condition.

Learn how to solve the inequality 3w - 16w - 19 ≥ 15 - 15w with a detailed step-by-step solution. This problem involves linear equations and inequalities, covering concepts like combining like terms and isolating variables. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation