Solve the compound inequality. 11−3x≥−7 and 3x−5≥1 (1 point)

Question

Responses
x≤6 and x≥2
x≥−4 and x≤3
x≥6 and x≥2
x≤43 and x≤2

Answer 1

To solve the compound inequality 11 - 3x ≥ -7 and 3x - 5 ≥ 1, we can solve each inequality separately and then find the intersection of the solution sets.

For the first inequality:
11 - 3x ≥ -7
Subtract 11 from both sides:
-3x ≥ -18
Divide both sides by -3, remembering to flip the inequality sign when dividing by a negative number:
x ≤ 6

For the second inequality:
3x - 5 ≥ 1
Add 5 to both sides:
3x ≥ 6
Divide both sides by 3:
x ≥ 2

Now, we can find the intersection of the solution sets:
The solution set for x in the first inequality is x ≤ 6.
The solution set for x in the second inequality is x ≥ 2.

Since both inequalities need to be satisfied, the intersection of the solution sets is x ≤ 6 and x ≥ 2.
Therefore, the correct response is x ≤ 6 and x ≥ 2.