What is the solution of 7 + m is greater than or equal to 2 and m + 1 is less than 2?
Please explain or show how you got the answer-I'm having a really hard time
To solve the inequality 7 + m ≥ 2 and m + 1 < 2, we need to find the values of m that satisfy both conditions simultaneously.
Let's solve each inequality separately:
1. 7 + m ≥ 2
To isolate the variable m, we subtract 7 from both sides:
7 + m - 7 ≥ 2 - 7
m ≥ -5
So, the first condition is satisfied when m is greater than or equal to -5.
2. m + 1 < 2
To isolate the variable m, we subtract 1 from both sides:
m + 1 - 1 < 2 - 1
m < 1
Now, let's compare the two solutions:
-5 < m < 1
This means that the values of m which satisfy both conditions are any value between -5 and 1, excluding -5 and including 1.
Mathematically, we can write the solution as:
-5 < m ≤ 1
So, the solution to the given inequality is m lies between -5 and 1, including -5 but not including 1.