Solve the compound inequality.
10 ≥ 7 + 3x and 9 - 4x ≤ 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
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.
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.