Solve the compound inequality  −4a+13≥29 and 10<6a−14
 

To solve the compound inequality, we need to solve each inequality separately and then find the intersection of the solutions.

### First Inequality:  
\[
-4a + 13 \geq 29
\]

1. Subtract 13 from both sides:
   \[
   -4a \geq 29 - 13
   \]
   \[
   -4a \geq 16
   \]

2. Divide both sides by -4, and remember to flip the inequality sign (since we are dividing by a negative number):
   \[
   a \leq \frac{16}{-4}
   \]
   \[
   a \leq -4
   \]

### Second Inequality:
\[
10 < 6a - 14
\]

1. Add 14 to both sides:
   \[
   10 + 14 < 6a
   \]
   \[
   24 < 6a
   \]

2. Divide both sides by 6:
   \[
   \frac{24}{6} < a
   \]
   \[
   4 < a \quad \text{or} \quad a > 4
   \]

### Combining the Results:

- From the first inequality: \( a \leq -4 \)
- From the second inequality: \( a > 4 \)

Since there is no overlap between \( a \leq -4 \) and \( a > 4 \), **there is no solution** for this compound inequality.

Would you like further details on any steps or explanations?

### Related Questions:
1. How do you solve compound inequalities with "and" vs "or" conditions?
2. What happens if the inequalities overlap?
3. Can compound inequalities have no solution in some cases?
4. How do we graph the solution of compound inequalities on a number line?
5. How does dividing or multiplying by negative numbers affect inequality signs?

**Tip:** Always pay attention to flipping the inequality sign when dividing or multiplying by negative numbers.

Solve the compound inequality −4a+13≥29 and 10<6a−14

This page provides a step-by-step solution to the compound inequality −4a+13≥29 and 10<6a−14. Learn about solving inequalities, flipping inequality signs when dividing by negatives, and interpreting results with no solution. 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