Which values from the set {−6, −4, −2, 0, 2, 4, 6} satisfy this inequality? 3 + 1 2 x ≥ 4 Responses A –6, –4, –2 and 0 only–6, –4, –2 and 0 only B 0, 2 and 4 only0, 2 and 4 only C 2, 4 and 6 only2, 4 and 6 only D –4, –2 and 0 only
To solve the inequality, we need to isolate the variable x. We first subtract 3 from both sides: 3 + (1/2)x ≥ 4 - 3, which simplifies to (1/2)x ≥ 1. We then multiply both sides by 2 to remove the fraction: 2 * (1/2)x ≥ 1 * 2, which simplifies to x ≥ 2.
Now we need to determine which values from the given set satisfy x ≥ 2. The values that are greater than or equal to 2 in the given set are 2, 4, and 6. Therefore, the answer is C: 2, 4, and 6 only.
whats the answer a b c or d
The answer is C: 2, 4, and 6 only.
To determine which values from the set {−6, −4, −2, 0, 2, 4, 6} satisfy the inequality 3 + (1/2)x ≥ 4, we need to solve the inequality and find the values of x that make it true.
Step 1: Start by subtracting 3 from both sides of the inequality to isolate the x term:
3 + (1/2)x - 3 ≥ 4 - 3
(1/2)x ≥ 1
Step 2: Multiply both sides of the inequality by 2 to remove the fraction:
2 * (1/2)x ≥ 1 * 2
x ≥ 2
We have found that x must be greater than or equal to 2 for the inequality to hold true.
Step 3: Now, we check each value in the set {−6, −4, −2, 0, 2, 4, 6} to see which satisfy x ≥ 2.
Let's check each value:
For -6: -6 is not greater than or equal to 2. So, -6 does not satisfy the inequality.
For -4: -4 is not greater than or equal to 2. So, -4 does not satisfy the inequality.
For -2: -2 is not greater than or equal to 2. So, -2 does not satisfy the inequality.
For 0: 0 is not greater than or equal to 2. So, 0 does not satisfy the inequality.
For 2: 2 is equal to 2. So, 2 satisfies the inequality.
For 4: 4 is greater than 2. So, 4 satisfies the inequality.
For 6: 6 is greater than 2. So, 6 satisfies the inequality.
From the above analysis, we can see that the values which satisfy the inequality x ≥ 2 are 2, 4, and 6.
Therefore, the correct answer is option C: 2, 4, and 6 only.