https://file.aiquickdraw.com/mathbot/file/1727454056199esyrcpei.jpg

The inequality to solve for \( q \) is:

\[
-2(8q + 3) \leq 8q - 5(5q + 16)
\]

Let's solve it step by step.

### Step 1: Expand both sides
- Left-hand side: \( -2(8q + 3) = -16q - 6 \)
- Right-hand side: \( -5(5q + 16) = -25q - 80 \)

So the inequality becomes:
\[
-16q - 6 \leq 8q - 25q - 80
\]

### Step 2: Simplify both sides
On the right-hand side:
\[
8q - 25q = -17q
\]

Now the inequality is:
\[
-16q - 6 \leq -17q - 80
\]

### Step 3: Move terms involving \( q \) to one side
Add \( 17q \) to both sides:
\[
-16q + 17q - 6 \leq -80
\]
\[
q - 6 \leq -80
\]

### Step 4: Isolate \( q \)
Add 6 to both sides:
\[
q \leq -74
\]

### Final Answer:
\[
q \leq -74
\]

Would you like further explanation or details? Here are some related questions:

1. How do we check if the solution \( q \leq -74 \) satisfies the original inequality?
2. What happens if we multiply or divide both sides of an inequality by a negative number?
3. Can you provide more examples involving inequality solving?
4. How does solving inequalities differ from solving equations?
5. How do we graph the solution of an inequality on a number line?

**Tip:** When solving inequalities, be careful when multiplying or dividing by negative numbers, as this reverses the inequality sign!

Solve for q: -2(8q + 3) ≤ 8q - 5(5q + 16)

Learn how to solve the linear inequality -2(8q + 3) ≤ 8q - 5(5q + 16) with a step-by-step solution. This problem covers key algebraic concepts such as the distributive property and properties of inequalities, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation