solve the below compound inequality

Question

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.
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Answer 1

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≤.