Which values from the set {−6, −4, −2, 0, 2, 4, 6} satisfy this inequality?
3 + 1/2 x ≥ 4
answers:
–6, –4, –2 and 0 only
0, 2 and 4 only
2, 4 and 6 only
–4, –2 and 0 only
To find the values that satisfy the inequality 3 + 1/2x ≥ 4, we need to solve it step-by-step.
First, subtract 3 from both sides of the inequality:
3 + 1/2x - 3 ≥ 4 - 3
This simplifies to:
1/2x ≥ 1
Next, multiply both sides of the inequality by 2 to get rid of the fraction:
2 * (1/2x) ≥ 2 * 1
This simplifies to:
x ≥ 2
Now, we have found that x should be greater than or equal to 2.
Out of the given set of values {−6, −4, −2, 0, 2, 4, 6}, the values that satisfy the inequality are:
2, 4, and 6 only.
So the correct answer is: 2, 4, and 6 only.
To find the values that satisfy the inequality, we can substitute each value from the set into the inequality and test if the inequality is true.
Substituting -6 into the inequality, we have:
3 + 1/2(-6) ≥ 4
3 - 3 ≥ 4
0 ≥ 4
The inequality is not true when x = -6.
Substituting -4 into the inequality, we have:
3 + 1/2(-4) ≥ 4
3 - 2 ≥ 4
1 ≥ 4
The inequality is not true when x = -4.
Substituting -2 into the inequality, we have:
3 + 1/2(-2) ≥ 4
3 - 1 ≥ 4
2 ≥ 4
The inequality is not true when x = -2.
Substituting 0 into the inequality, we have:
3 + 1/2(0) ≥ 4
3 + 0 ≥ 4
3 ≥ 4
The inequality is not true when x = 0.
Substituting 2 into the inequality, we have:
3 + 1/2(2) ≥ 4
3 + 1 ≥ 4
4 ≥ 4
The inequality is true when x = 2.
Substituting 4 into the inequality, we have:
3 + 1/2(4) ≥ 4
3 + 2 ≥ 4
5 ≥ 4
The inequality is true when x = 4.
Substituting 6 into the inequality, we have:
3 + 1/2(6) ≥ 4
3 + 3 ≥ 4
6 ≥ 4
The inequality is true when x = 6.
From our calculations, we can see that the values 2, 4, and 6 satisfy the inequality. Therefore, the correct answer is:
2, 4 and 6 only
To find the values that satisfy the inequality, we can plug each value from the given set into the inequality and check if it is true.
The inequality is:
3 + (1/2)x ≥ 4
Let's check each value in the set:
For x = -6:
3 + (1/2)(-6) = 3 - 3 = 0
0 ≥ 4 is not true.
For x = -4:
3 + (1/2)(-4) = 3 - 2 = 1
1 ≥ 4 is not true.
For x = -2:
3 + (1/2)(-2) = 3 - 1 = 2
2 ≥ 4 is not true.
For x = 0:
3 + (1/2)(0) = 3 + 0 = 3
3 ≥ 4 is not true.
For x = 2:
3 + (1/2)(2) = 3 + 1 = 4
4 ≥ 4 is true.
For x = 4:
3 + (1/2)(4) = 3 + 2 = 5
5 ≥ 4 is true.
For x = 6:
3 + (1/2)(6) = 3 + 3 = 6
6 ≥ 4 is true.
From the calculations above, the values that satisfy the inequality are:
2, 4, and 6 only.
Therefore, the correct answer is:
2, 4, and 6 only.