Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App Chapter 1: Q40. (page 44)
Solve each inequality. Graph the solution set on a number line.
Short Answer
Given inequality has no solution
The solution set in the number line is empty
Step by step solution
- Definition of absolute value inequality
For real numbers with
Absolute value inequality is when , and
Absolute value inequality is when
- Write properties of inequality
Properties of inequalities are written in the following table:
- Simplify 7x+4<0
Use subtraction property of inequality, subtracting with the same number does not change the sign of inequality as shown below
From the definition of absolute value, it is the distance of a point from 0, so it is always greater than or equal to 0. But in the given expression, the absolute value is less than 0 so it has no solution.
- Graph the solution set
As given expression has no solution set, so it cannot be represented on the number line.
Thus, there is no solution on the number line, so it is empty.
Over 30 million students worldwide already upgrade their learning with Vaia!
