Which values from the set satisfy the inequality?
{ 0, 3, 5, 6, 9 }
3x - 4 ≤ 15
A) 0, 3, 5, 6 ****
B) 3, 5, 6
C) 3, 5
D) 5, 6, 9
correct
thx
To solve the inequality 3x - 4 ≤ 15, we need to find the values of x that satisfy the inequality.
Let's go through the given choices and substitute each value for x to check if the inequality is true or false.
Choice A) 0, 3, 5, 6:
- For x = 0: 3(0) - 4 ≤ 15, which is true because -4 ≤ 15.
- For x = 3: 3(3) - 4 ≤ 15, which is true because 5 ≤ 15.
- For x = 5: 3(5) - 4 ≤ 15, which is true because 11 ≤ 15.
- For x = 6: 3(6) - 4 ≤ 15, which is true because 14 ≤ 15.
Choice A includes all the values for x that satisfy the inequality, so the correct choice is A) 0, 3, 5, 6.
To determine which values from the set {0, 3, 5, 6, 9} satisfy the inequality 3x - 4 ≤ 15, we need to substitute each value into the inequality and check if it holds true. Let's go through each option:
A) 0, 3, 5, 6:
- For 0: 3(0) - 4 = -4, which is less than or equal to 15. So, 0 satisfies the inequality.
- For 3: 3(3) - 4 = 5, which is less than or equal to 15. So, 3 satisfies the inequality.
- For 5: 3(5) - 4 = 11, which is less than or equal to 15. So, 5 satisfies the inequality.
- For 6: 3(6) - 4 = 14, which is less than or equal to 15. So, 6 satisfies the inequality.
B) 3, 5, 6:
- For 3, 5, and 6, we have already checked that they satisfy the inequality.
C) 3, 5:
- We have already checked that both 3 and 5 satisfy the inequality.
D) 5, 6, 9:
- For 5: 3(5) - 4 = 11, which is less than or equal to 15. So, 5 satisfies the inequality.
- For 6: 3(6) - 4 = 14, which is less than or equal to 15. So, 6 satisfies the inequality.
- For 9: 3(9) - 4 = 23, which is not less than or equal to 15. So, 9 does not satisfy the inequality.
Considering the above analysis, the correct answer is option A) 0, 3, 5, 6, as all these values satisfy the inequality 3x - 4 ≤ 15.