Question

Solve the compound inequality.

10 ≥ 7 + 3x and 9 - 4x ≤ 1

Answer 1

wrong again. Clearly, x=3 does not work in 10 ≥ 7 + 3x
In fact, there is no number x such that x < 1 and x > 2

Answer 2

To solve the compound inequality, we will first solve each inequality separately and then combine the solutions.

1) Solve 10 ≥ 7 + 3x:
Subtract 7 from both sides:
3 ≥ 3x
Divide by 3:
1 ≥ x

2) Solve 9 - 4x ≤ 1:
Subtract 9 from both sides:
-4x ≤ -8
Divide by -4 (remember to flip the inequality sign when dividing by a negative number):
x ≥ 2

Now we have the individual solutions x ≤ 1 and x ≥ 2. To combine these into one solution, we need to find the intersection of the two intervals, which is x ≥ 2.

Therefore, the solution to the compound inequality is x ≥ 2.

Answer 3

I apologize for the error in my previous response. Let's correct that:

1) Solve 10 ≥ 7 + 3x:
Subtract 7 from both sides:
3 ≥ 3x
Divide by 3:
1 ≥ x

2) Solve 9 - 4x ≤ 1:
Subtract 9 from both sides:
-4x ≤ -8
Divide by -4 (remember to flip the inequality sign when dividing by a negative number):
x ≥ 2

Now, the correct set of solutions for each inequality is x ≤ 1 and x ≥ 2. To find the intersection of the two sets, we look for the values that satisfy both inequalities. However, as you correctly pointed out, there is no number x that is simultaneously less than or equal to 1 and greater than or equal to 2.

Therefore, the solution to the compound inequality is the empty set, as there are no values of x that satisfy both inequalities at the same time. Thank you for pointing out the mistake.