How to solve the compound inequalities of.
-1< 3+2x<11 1 – x >-3 or 5x-1>19
I will assume I am looking at two different ones
1.
-1< 3+2x<11
2.
1 – x >-3 or 5x-1>19
#1.
-1< 3+2x<11
subtract 3
-4 ≤ 2x < 8
divide by 2
-2 < x < 4
all real numbers between -2 and 4
#2
1 – x >-3 or 5x-1>19
-x > -4 or 5x > 20
x < 4 or x > 4
mmmh, looks like all real numbers except x = 4
To solve compound inequalities, we need to break them down into individual inequalities and solve each one separately. Let's break down the given compound inequalities and solve them one by one.
1. -1 < 3 + 2x < 11:
We have three parts in this compound inequality: -1 < 3 + 2x and 3 + 2x < 11.
Starting with -1 < 3 + 2x:
1. Subtract 3 from both sides: -1 - 3 < 3 + 2x - 3
Simplifying gives: -4 < 2x
2. Divide both sides by 2:
-4/2 < 2x/2
Simplifying gives: -2 < x
So, the first part of the compound inequality is -2 < x.
Now let's solve 3 + 2x < 11:
1. Subtract 3 from both sides: 3 + 2x - 3 < 11 - 3
Simplifying gives: 2x < 8
2. Divide both sides by 2:
2x/2 < 8/2
Simplifying gives: x < 4
So, the second part of the compound inequality is x < 4.
Therefore, the solution to the compound inequality -1 < 3 + 2x < 11 is -2 < x < 4.
2. 1 - x > -3 or 5x - 1 > 19:
We have two parts in this compound inequality: 1 - x > -3 and 5x - 1 > 19.
Starting with 1 - x > -3:
1. Add x to both sides: 1 - x + x > -3 + x
Simplifying gives: 1 > -3 + x
2. Add 3 to both sides: 1 + 3 > -3 + x + 3
Simplifying gives: 4 > x
So, the first part of the compound inequality is x < 4.
Now let's solve 5x - 1 > 19:
1. Add 1 to both sides: 5x - 1 + 1 > 19 + 1
Simplifying gives: 5x > 20
2. Divide both sides by 5:
5x/5 > 20/5
Simplifying gives: x > 4
So, the second part of the compound inequality is x > 4.
Therefore, the solution to the compound inequality 1 - x > -3 or 5x - 1 > 19 is x < 4 or x > 4.