To calculate: The solution of the compound inequality -2\left(x-1\right)+4<x+3\ \text

mronjo7n

mronjo7n

Answered question

2021-11-22

To calculate: The solution of the compound inequality
2(x1)+4<x+3 r 5(x+2)34x+r 5(x+2)34x+1
and graph the solution set and write the solution set in interval notation.

Answer & Explanation

jackbranv5

jackbranv5

Beginner2021-11-23Added 8 answers

Given information:
The compound inequality,-2x-1+4<x+3 r 5x+2-34x+r 5x+2-34x+1.
Formula used:
Steps to solve compound inequality:
Step 1: First, solve the compound inequality individually.
Step 2: If two inequalities are combined through “or’/“and” then take the union/intersection, respectively, of individual solution set.
Calculation:
The given compound inequality is 

-2x-1+4<x+3 r 5x+2-34x+r 5x+2-34x+1. Simplify the inequality.
-2x-1+4<x+3 r 5x+2-34x+r 5x+2-34x+1
-2x+2+4<x+3 r 5x+10-34x+r 5x+10-34x+1
-2x-x<3-6 r 5x-4x1-r 5x-4x1-7
x>1 r x-r x-6
Therefore, the solution set of compound inequalit-2x-1+4<x+3 r 5x+2-34x+r 5x+2-34x+1in interval notation is:
((--6)(1,)

Thomas Conway

Thomas Conway

Beginner2021-11-24Added 10 answers

Given information:
The compound inequality, -2x-1+4<x+3 or 5x+2-34x+1.
Formula used:
Steps to solve compound inequality:
Step 1: First, solve the compound inequality individually.
Step 2: If two inequalities are combined through “or’/“and” then take the union/intersection, respectively, of individual solution set.
Calculation:
The given compound inequality is -2x-1+4<x+3 or 5x+2-34x+1. Simplify the inequality.
-2x-1+4<x+3 or 5x+2-34x+1
-2x+2+4<x+3 or 5x+10-34x+1
-2x-x<3-6 or 5x-4x1-7
x>1 or x-6
The graph of the solution is:
image
Therefore, the solution set of compound inequality-2x-1+4<x+3 or 5x+2-34x+1in interval notation is: 
 

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