The numbers 5, 6, and 7 are solutions of which of the following inequalities?(1 point)
Responses
3x−4>11
3 x minus 4 greater than 11
3x+4≥16
3 x plus 4 greater-than-or-equal-to 16
15−x<10
15 minus x less than 10
x+10≠15
To find the inequality that the numbers 5, 6, and 7 are solutions of, we can substitute each number into the inequalities and see which one is satisfied.
1) 3x - 4 > 11
Substituting 5, 6, and 7:
For x = 5: 3(5) - 4 = 15 - 4 = 11 (not greater than 11)
For x = 6: 3(6) - 4 = 18 - 4 = 14 (greater than 11)
For x = 7: 3(7) - 4 = 21 - 4 = 17 (greater than 11)
2) 3x + 4 ≥ 16
Substituting 5, 6, and 7:
For x = 5: 3(5) + 4 = 15 + 4 = 19 (greater than or equal to 16)
For x = 6: 3(6) + 4 = 18 + 4 = 22 (greater than or equal to 16)
For x = 7: 3(7) + 4 = 21 + 4 = 25 (greater than or equal to 16)
3) 15 - x < 10
Substituting 5, 6, and 7:
For x = 5: 15 - 5 = 10 (less than 10)
For x = 6: 15 - 6 = 9 (less than 10)
For x = 7: 15 - 7 = 8 (less than 10)
4) x + 10 ≠ 15
Substituting 5, 6, and 7:
For x = 5: 5 + 10 = 15 (not not equal to 15, so it is equal)
For x = 6: 6 + 10 = 16 (not not equal to 15, so it is equal)
For x = 7: 7 + 10 = 17 (not not equal to 15, so it is equal)
Therefore, the numbers 5, 6, and 7 are solutions of the inequality 3x + 4 ≥ 16.