https://file.aiquickdraw.com/mathbot/file/1726278742582dxo5tzaa.jpg

https://file.aiquickdraw.com/mathbot/file/1726278742582ao9h60bq.jpg

Let's go through each of the questions one by one and solve the inequalities.

### **Question 13**
Given inequalities:
1. \( 2t - 15 < 3t - 17 \)
2. \( t - 13 < -19 \)

**Step 1: Solve each inequality**

1. **First inequality:** \( 2t - 15 < 3t - 17 \)

   Subtract \( 2t \) from both sides:
   \[
   -15 < t - 17
   \]

   Add 17 to both sides:
   \[
   2 < t
   \]

2. **Second inequality:** \( t - 13 < -19 \)

   Add 13 to both sides:
   \[
   t < -6
   \]

**Step 2: Combine the inequalities**

The inequalities to satisfy are \( 2 < t \) and \( t < -6 \). Since there's no number that can simultaneously satisfy both \( t > 2 \) and \( t < -6 \), there is **no solution** for this system.

### **Question 14**
Given inequalities:
1. \( 3d + 17 \leq 11 \)
2. \( -4d + 4 < -3d + 24 \)

**Step 1: Solve each inequality**

1. **First inequality:** \( 3d + 17 \leq 11 \)

   Subtract 17 from both sides:
   \[
   3d \leq -6
   \]

   Divide by 3:
   \[
   d \leq -2
   \]

2. **Second inequality:** \( -4d + 4 < -3d + 24 \)

   Add \( 4d \) to both sides:
   \[
   4 < d + 24
   \]

   Subtract 24 from both sides:
   \[
   -20 < d
   \]

**Step 2: Combine the inequalities**

The compound inequality from both parts is:
\[
-20 < d \quad \text{or} \quad d \leq -2
\]

This means the solution is \( d \in (-20, \infty) \) excluding the interval \((-2, -20]\).

### **Question 15**


In Exercises 12–15, solve the inequality. Graph the solution, if possible.

Step-by-step solution for solving compound inequalities involving linear equations. Learn how to solve inequalities like 2t - 15 < 3t - 17 and t - 13 < -19 and how to graph the solution. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation