Solve the compound inequality.
5x + 7 ≤ - 8 and 4x ≤0
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
• A.
The solution is X≤
• В.
The solution is
=X≤
• C.
The solution is x≥
• D.
The solution is x=
• E. The solution is all real numbers
OF. There is no solution.
To solve the compound inequality, we will solve each inequality separately and then find the intersection of their solutions.
First, let's solve the inequality 5x + 7 ≤ -8:
Subtract 7 from both sides: 5x ≤ -15
Divide both sides by 5: x ≤ -3
Next, let's solve the inequality 4x ≤ 0:
Divide both sides by 4: x ≤ 0
Now, we need to find the intersection of the solutions x ≤ -3 and x ≤ 0. This means we need to find the values of x that satisfy both inequalities.
Since x ≤ -3 includes all values less than or equal to -3, and x ≤ 0 includes all values less than or equal to 0, the intersection of the two solutions is x ≤ -3.
Therefore, the correct answer is A. The solution is x ≤ -3.