https://file.aiquickdraw.com/mathbot/file/1727268334020pt5x8cwk.jpg

I can help you solve the inequalities shown in the image. Let's go through them one by one and solve each inequality:

### 1. \(-10n - 6 > 74\)
Solve for \(n\):
\[
-10n > 74 + 6
\]
\[
-10n > 80
\]
Divide both sides by \(-10\), remembering to flip the inequality sign when dividing by a negative number:
\[
n < -8
\]
Graph: The solution will be all values less than \(-8\), represented by an open circle on \(-8\) and shading to the left.

---

### 2. \(|8n - 5| \leq 59\)
For absolute value inequalities, split it into two inequalities:
\[
-59 \leq 8n - 5 \leq 59
\]
Solve both:
1. \(8n - 5 \geq -59\):
\[
8n \geq -59 + 5 \implies 8n \geq -54 \implies n \geq -\frac{54}{8} = -6.75
\]
2. \(8n - 5 \leq 59\):
\[
8n \leq 59 + 5 \implies 8n \leq 64 \implies n \leq 8


Solve each inequality and graph its solution (various inequalities involving absolute values and linear equations).

This assignment covers solving inequalities, including absolute value inequalities, and graphing the solutions on a number line. Learn how to manipulate and solve inequalities step by step, with visual representation of the solution. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation