I’m the inequality what are all the possible values of x? -8x+6_< 2(-3x+1). A. X_>2 b. x_< 2 c. x> 1/2 d. x< -1
First, let's simplify the inequality:
-8x + 6 ≤ 2(-3x + 1)
-8x + 6 ≤ -6x + 2
To solve for x, we need to isolate it. Let's subtract -6x from both sides:
-8x + 6 + 6x ≤ -6x + 2 - 6x
-2x + 6 ≤ -12x + 2
Next, let's add 12x to both sides:
-2x + 12x + 6 ≤ -12x + 12x + 2
10x + 6 ≤ 2
Then, subtract 6 from both sides:
10x + 6 - 6 ≤ 2 - 6
10x ≤ -4
Finally, divide both sides by 10:
(10x)/10 ≤ (-4)/10
x ≤ -4/10
x ≤ -2/5
So, the solution is x ≤ -2/5.
However, none of the given options matches this solution. Therefore, none of the options is correct.
To solve the inequality -8x + 6 ≤ 2(-3x + 1), we can follow these steps:
Step 1: Distribute the 2 on the right side of the inequality:
-8x + 6 ≤ -6x + 2
Step 2: Combine like terms:
-8x + 6x ≤ 2 - 6
Step 3: Simplify the inequality:
-2x ≤ -4
Step 4: Divide both sides of the inequality by -2. Remember to reverse the inequality when dividing by a negative number:
x ≥ 2
Therefore, the correct answer is:
A. x ≥ 2
To find the possible values of x for the given inequality -8x + 6 ≤ 2(-3x + 1), we need to simplify and solve for x.
Let's start by distributing the 2 on the right side of the inequality:
-8x + 6 ≤ -6x + 2
Next, we can rearrange the terms by moving the -6x to the left side and the 6 to the right side:
-8x + 6x ≤ 2 - 6
Simplifying further:
-2x ≤ -4
Now, we will divide both sides of the inequality by -2. When we divide by a negative number, the inequality sign flips, so we have:
x ≥ 2
So, the possible values of x for the given inequality are x ≥ 2.
Therefore, the correct answer is option A. x ≥ 2.