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
x + 3 < 4(x + 1) + 2 (false)
2x - 8 ≥ 7 - 3x (false)
3(x + 2) < 14 - x (true)
4(x - 1) < x + 5 (true)
5 - 2( x + 1) > x (true)
6(x - 4) ≤ 2x (false)
Therefore, the inequalities with x = 3 as a solution are:
3(x + 2) < 14 - x
4(x - 1) < x + 5
5 - 2( x + 1) > x.
The inequality with x = 3 as a solution is:
x + 3 < 4(x + 1) + 2
To identify the inequality with x = 3 as a solution, we need to substitute x = 3 into each inequality and check if it holds true. Let's go through each option and evaluate them:
1) x + 3 < 4(x + 1) + 2
Substituting x = 3:
3 + 3 < 4(3 + 1) + 2
6 < 4(4) + 2
6 < 16 + 2
6 < 18
This inequality is false since 6 is not less than 18.
2) 2x - 8 ≥ 7 - 3x
Substituting x = 3:
2(3) - 8 ≥ 7 - 3(3)
6 - 8 ≥ 7 - 9
-2 ≥ -2
This inequality is true since -2 is indeed greater than or equal to -2.
3) 3(x + 2) < 14 - x
Substituting x = 3:
3(3 + 2) < 14 - 3
15 < 14 - 3
15 < 11
This inequality is false since 15 is not less than 11.
4) 4(x - 1) < x + 5
Substituting x = 3:
4(3 - 1) < 3 + 5
4(2) < 8
8 < 8
This inequality is false since 8 is not less than 8.
5) 5 - 2(x + 1) > x
Substituting x = 3:
5 - 2(3 + 1) > 3
5 - 2(4) > 3
5 - 8 > 3
-3 > 3
This inequality is false since -3 is not greater than 3
6) 6(x - 4) ≤ 2x
Substituting x = 3:
6(3 - 4) ≤ 2(3)
6(-1) ≤ 6
-6 ≤ 6
This inequality is true since -6 is indeed less than or equal to 6.
From the above evaluations, the inequalities that hold true for x = 3 are:
2x - 8 ≥ 7 - 3x
6(x - 4) ≤ 2x
Therefore, the options 2) and 6) are the correct inequalities with x = 3 as a solution.