Solve. 5 < x – 2 < 11
To solve the inequality, we will break it up into two separate inequalities and solve each one separately.
First, let's solve for the left inequality: 5 < x - 2.
Adding 2 to both sides, we get: 7 < x.
Now, let's solve for the right inequality: x - 2 < 11.
Adding 2 to both sides, we get: x < 13.
Therefore, the solution to the original inequality is 7 < x < 13.
To solve the inequality, we need to isolate the variable "x" in the middle.
Step 1: Add 2 to all sides of the inequality:
5 + 2 < x – 2 + 2 < 11 + 2
Simplifying this gives:
7 < x < 13
Hence, the solution to the inequality is 7 < x < 13.
To solve the compound inequality 5 < x - 2 < 11, we need to isolate the variable, x, and find the range of values that satisfy the inequality.
Let's break it down:
Starting inequality: 5 < x - 2 < 11
First, add 2 to all three parts of the inequality:
5 + 2 < x - 2 + 2 < 11 + 2
This simplifies to:
7 < x < 13
So, the solution to the inequality is x lying between 7 and 13, excluding the endpoints. This can be represented as the open interval (7, 13).