solve the below compound inequality
x+7≥1 and 7x-4≥3
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice
0 A.
The solution is
≤X≤
O B. The solution is X≤
O c. The solution is X≥
Or X≤
• D.
The solution Is x=
• E.
The solution is all real numbers
• F.
There is no solution.
Help me solve this View
To solve the compound inequality, we will solve both inequalities separately and then determine the overlapping solution.
First, let's solve the first inequality: x + 7 ≥ 1.
Subtract 7 from both sides:
x + 7 - 7 ≥ 1 - 7
x ≥ -6
Now, let's solve the second inequality: 7x -4 ≥ 3.
Add 4 to both sides:
7x - 4 + 4 ≥ 3 + 4
7x ≥ 7
Divide both sides by 7:
x ≥ 1
Now we will determine the overlapping solution between x ≥ -6 and x ≥ 1. The overlapping range is x ≥ 1 since -6 is not greater than or equal to 1.
Therefore, the correct choice is:
B. The solution is X≤.