Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter5: Linear Inequalities
Section: Chapter Questions
Problem 6SGR
Related questions
Question
![**Solving and Graphing the Inequality**
The problem presents an inequality that needs to be solved, graphed, and written in interval notation. The given inequality is:
\[ -11 < y - 1 \leq -1 \]
### Step a) Solve
To solve the inequality, we need to isolate the variable \( y \). We will do this in two steps for both parts of the compound inequality.
1. **First Part of the Compound Inequality: \( -11 < y - 1 \)**
Add 1 to both sides:
\[ -11 + 1 < y - 1 + 1 \]
Simplify:
\[ -10 < y \]
2. **Second Part of the Compound Inequality: \( y - 1 \leq -1 \)**
Add 1 to both sides:
\[ y - 1 + 1 \leq -1 + 1 \]
Simplify:
\[ y \leq 0 \]
Combining both parts, we get the solution:
\[ -10 < y \leq 0 \]
### Step b) Graph
To graph this solution, we draw a number line and mark the interval from -10 to 0.
1. Use an open circle at -10 to indicate that -10 is not included in the solution (\( -10 < y \)).
2. Use a closed circle at 0 to indicate that 0 is included in the solution (\( y \leq 0 \)).
3. Shade the region between -10 and 0 to show all the values that satisfy the inequality:
\[
-10 \ \mathring{} \ \ \ \text{-----------------------------------[0]}
\]
### Step c) Write the Solution in Interval Notation
In interval notation, the solution is written as:
\[ (-10, 0] \]
This notation indicates that the interval starts from -10 (but does not include -10) and goes up to 0 (including 0).
---
This completes the solution, graph, and interval notation representation of the given inequality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c1b1525-9f55-427c-9418-433680b9f4b9%2F4c92b360-29e5-49d2-9b99-160b472366f7%2Fqfq3tcb_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving and Graphing the Inequality**
The problem presents an inequality that needs to be solved, graphed, and written in interval notation. The given inequality is:
\[ -11 < y - 1 \leq -1 \]
### Step a) Solve
To solve the inequality, we need to isolate the variable \( y \). We will do this in two steps for both parts of the compound inequality.
1. **First Part of the Compound Inequality: \( -11 < y - 1 \)**
Add 1 to both sides:
\[ -11 + 1 < y - 1 + 1 \]
Simplify:
\[ -10 < y \]
2. **Second Part of the Compound Inequality: \( y - 1 \leq -1 \)**
Add 1 to both sides:
\[ y - 1 + 1 \leq -1 + 1 \]
Simplify:
\[ y \leq 0 \]
Combining both parts, we get the solution:
\[ -10 < y \leq 0 \]
### Step b) Graph
To graph this solution, we draw a number line and mark the interval from -10 to 0.
1. Use an open circle at -10 to indicate that -10 is not included in the solution (\( -10 < y \)).
2. Use a closed circle at 0 to indicate that 0 is included in the solution (\( y \leq 0 \)).
3. Shade the region between -10 and 0 to show all the values that satisfy the inequality:
\[
-10 \ \mathring{} \ \ \ \text{-----------------------------------[0]}
\]
### Step c) Write the Solution in Interval Notation
In interval notation, the solution is written as:
\[ (-10, 0] \]
This notation indicates that the interval starts from -10 (but does not include -10) and goes up to 0 (including 0).
---
This completes the solution, graph, and interval notation representation of the given inequality.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL