In the inequality, what are all the possible values of x?
-8x + 6 ≤ 2(-3x + 1)
A. X ≥ 2
B. × ≤ 2
C. x > 1/2
D. X < -1
To find the possible values of x, let's solve the inequality step by step:
-8x + 6 ≤ 2(-3x + 1)
Starting from the right side:
-8x + 6 ≤ -6x + 2
Rearranging the terms:
-8x + 6x ≤ 2 - 6
-2x ≤ -4
Dividing both sides by -2 (Note: When dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips):
x ≥ 2
Therefore, the possible values of x are x ≥ 2.
So, the correct answer is:
A. x ≥ 2
To solve this inequality step-by-step, we'll begin by simplifying both sides of the equation:
-8x + 6 ≤ 2(-3x + 1)
Distribute the 2 to both terms inside the parentheses:
-8x + 6 ≤ -6x + 2
Next, we'll move the variable terms to one side and the constant terms to the other side. Let's do this by subtracting -6x from both sides:
-8x + 6 + 6x ≤ -6x + 6x + 2
Simplifying:
-2x + 6 ≤ 2
Now, subtract 6 from both sides:
-2x + 6 - 6 ≤ 2 - 6
Simplifying:
-2x ≤ -4
Next, divide each side by -2. Remember that when you divide or multiply both sides of an inequality by a negative number, the inequality sign must be reversed:
-2x/-2 ≥ -4/-2
Simplifying:
x ≥ 2
So, the possible values of x that satisfy the inequality are x ≥ 2. Therefore, the correct answer is:
A. x ≥ 2
To find all the possible values of x in the given inequality, we need to solve it step by step. Let's start:
-8x + 6 ≤ 2(-3x + 1)
First, distribute the 2 on the right side:
-8x + 6 ≤ -6x + 2
Next, combine like terms by moving -6x from the right side to the left side:
-8x + 6x ≤ 2 - 6
-2x ≤ -4
Now, divide both sides of the inequality by -2. Remember, when dividing by a negative number, the direction of the inequality changes:
x ≥ 2
So, the correct answer is A. x ≥ 2.