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.
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.
1 answer