Which inequality represents the solution set for the compound inequality below?
-3<or equal to -2x + 1 < 11
3 >or= 2x -1 > -11
4 >or= 2x > -10
2 >or= x > -5
To find the inequality that represents the solution set for the compound inequality -3 ≤ -2x + 1 < 11, we have to solve it step-by-step.
Step 1: Subtract 1 from all parts of the inequality:
-3 - 1 ≤ -2x + 1 - 1 < 11 - 1
This simplifies to:
-4 ≤ -2x < 10
Step 2: Divide all parts of the inequality by -2. Since we are dividing by a negative number, we need to reverse the inequality signs:
-4 / -2 ≥ x > 10 / -2
This simplifies to:
2 ≥ x > -5
The inequality that represents the solution set for the compound inequality -3 ≤ -2x + 1 < 11 is:
-5 < x ≤ 2
To find the inequality that represents the solution set for the compound inequality -3 ≤ -2x + 1 < 11, we will break it down into two separate inequalities and solve for x.
First, let's isolate the middle term -2x + 1:
-3 ≤ -2x + 1 < 11
To remove the constant term 1, we subtract 1 from all parts of the compound inequality:
-3 - 1 ≤ -2x + 1 - 1 < 11 - 1
-4 ≤ -2x < 10
Next, divide all parts of the compound inequality by -2. Since we are dividing by a negative number, the inequality signs reverse:
-4/-2 ≥ -2x/-2 > 10/-2
2 ≥ x > -5
Therefore, the solution set for the compound inequality -3 ≤ -2x + 1 < 11 is x > -5 and x ≤ 2.
In inequality notation, the solution can be written as -5 < x ≤ 2.