Identify the inequality with x = 3 as a solution. Select all that apply.(3 points)
Responses
x + 3 < 4(x + 1) + 2
x + 3 < 4(x + 1) + 2
2x - 8 ≥ 7 - 3x
2x - 8 ≥ 7 - 3x
3(x + 2) < 14 - x
3(x + 2) < 14 - x
4(x - 1) < x + 5
4(x - 1) < x + 5
5 - 2( x + 1) > x
5 - 2( x + 1) > x
6(x - 4) ≤ 2x
6(x - 4) ≤ 2x
Identify the inequality with x = 3 as a solution. Select all that apply.(3 points)
Responses
x + 3 < 4(x + 1) + 2
x + 3 < 4(x + 1) + 2
2x - 8 ≥ 7 - 3x
2x - 8 ≥ 7 - 3x
3(x + 2) < 14 - x
3(x + 2) < 14 - x
4(x - 1) < x + 5
4(x - 1) < x + 5
5 - 2( x + 1) > x
5 - 2( x + 1) > x
Identify the inequality with x = 3 as a solution. Select all that apply.(3 points)
Responses
x + 3 < 4(x + 1) + 2
2x - 8 ≥ 7 - 3x
3(x + 2) < 14 - x
4(x - 1) < x + 5
5 - 2( x + 1) > x
6(x - 4) ≤ 2x
x + 3 < 4(x + 1) + 2
To identify the inequality with x = 3 as a solution, we can substitute x = 3 into each inequality and see which ones result in a true statement. Let's try each option one by one:
1) x + 3 < 4(x + 1) + 2
Substituting x = 3, we get: 3 + 3 < 4(3 + 1) + 2
6 < 4(4) + 2
6 < 16 + 2
6 < 18
This is false, so x = 3 is not a solution to this inequality.
2) 2x - 8 ≥ 7 - 3x
Substituting x = 3, we get: 2(3) - 8 ≥ 7 - 3(3)
6 - 8 ≥ 7 - 9
-2 ≥ -2
This is true, so x = 3 is a solution to this inequality.
3) 3(x + 2) < 14 - x
Substituting x = 3, we get: 3(3 + 2) < 14 - 3
3(5) < 11
15 < 11
This is false, so x = 3 is not a solution to this inequality.
4) 4(x - 1) < x + 5
Substituting x = 3, we get: 4(3 - 1) < 3 + 5
4(2) < 8
8 < 8
This is false, so x = 3 is not a solution to this inequality.
5) 5 - 2(x + 1) > x
Substituting x = 3, we get: 5 - 2(3 + 1) > 3
5 - 2(4) > 3
5 - 8 > 3
-3 > 3
This is false, so x = 3 is not a solution to this inequality.
6) 6(x - 4) ≤ 2x
Substituting x = 3, we get: 6(3 - 4) ≤ 2(3)
6(-1) ≤ 6
-6 ≤ 6
This is true, so x = 3 is a solution to this inequality.
Therefore, the inequalities with x = 3 as a solution are:
2x - 8 ≥ 7 - 3x
6(x - 4) ≤ 2x
So the correct answers are options 2 and 6.