-10 < -2 + 8x < 22
4x + 7 < 11 or 1 ¨C x ¡Ü -2
Please help me solve these compound inequalities. Any instruction would be appreciated.
-10 < -2 + 8x < 22
add 2
-8 < 8x < 24
divide by +8 , (no change in inequality sign)
-1 < x < 3
Can't make out your symbols in the 2nd
e.g. use <= for ≤ and >= for ≥
I apologize for the formatting error.
Here it is. Thanks for the help.
4x + 7 < 11 or 1 – x ≤ -2
-10 < -2 + 8x < 22 compound inequalities
To solve compound inequalities, we'll break it down into solving each individual inequality separately and then combining the results.
Let's start with the first compound inequality: -10 < -2 + 8x < 22.
1. Subtract -2 from all sides of the inequality: -10 + 2 < 8x < 22 + 2.
Simplifying this gives: -8 < 8x < 24.
2. Divide all sides of the inequality by 8: (-8)/8 < (8x)/8 < 24/8.
This simplifies to: -1 < x < 3.
So, the solution for the first compound inequality is -1 < x < 3.
Now, let's move on to the second compound inequality: 4x + 7 < 11 or 1 - x ≤ -2.
1. Solve the first inequality: 4x + 7 < 11.
Subtract 7 from both sides: 4x < 11 - 7.
Simplifying this gives: 4x < 4.
Divide by 4 on both sides: (4x)/4 < 4/4.
This simplifies to: x < 1.
So, the solution for the first inequality is x < 1.
2. Solve the second inequality: 1 - x ≤ -2.
Add x to both sides: 1 ≤ -2 + x.
Simplifying this gives: 1 ≤ x - 2.
Add 2 to both sides: 1 + 2 ≤ x.
Simplifying this gives: 3 ≤ x.
So, the solution for the second inequality is x ≥ 3.
To combine the solutions from both inequalities, we can use the "or" condition.
To represent the combined solution, we can write it as: x < 1 or x ≥ 3.
So, the solution to the compound inequality 4x + 7 < 11 or 1 - x ≤ -2 is x < 1 or x ≥ 3.