In the inequality what are all the possible values of x? -8x+6_<2(-3x+1)
To solve this inequality, we need to simplify both sides and isolate the variable x.
Starting on the left-hand side:
-8x + 6
And on the right-hand side:
2(-3x + 1) = -6x + 2
Thus, the inequality becomes:
-8x + 6 ≤ -6x + 2
Let's isolate the variable x by subtracting -6x from both sides:
-8x + 6 + 6x ≤ -6x + 2 - 6x
Combine like terms:
-2x + 6 ≤ 2 - 12x
Next, let's isolate the x terms on one side and the constants on the other side.
Add 2x and 12x to both sides:
-2x + 2x + 6 + 12x ≤ 2 - 12x + 12x
Combine like terms:
14x + 6 ≤ 2
Subtract 6 from both sides:
14x + 6 - 6 ≤ 2 - 6
Combine like terms:
14x ≤ -4
Finally, divide both sides by 14 to isolate x:
(14x)/14 ≤ -4/14
x ≤ -2/7
Thus, all the possible values of x satisfying the inequality -8x + 6 ≤ 2(-3x + 1) are values less than or equal to -2/7.
Therefore, x ≤ -2/7.
To find the possible values of x in the given inequality, let's simplify it step by step:
Step 1: Distribute the 2 on the right side of the inequality.
-8x + 6 ≤ -6x + 2
Step 2: Move the variables (x) to the left side of the inequality and the constants to the right side.
-8x + 6x ≤ 2 - 6
Step 3: Combine like terms.
-2x ≤ -4
Step 4: Divide both sides by -2. Since we are dividing by a negative number, the inequality sign changes direction.
x ≥ 2
So, the possible values of x in the given inequality are x ≥ 2.
To find all the possible values of x in the inequality -8x + 6 ≤ 2(-3x + 1), we will solve it step by step:
Step 1: Distribute the 2 on the right side of the equation: -8x + 6 ≤ -6x + 2.
Step 2: Rearrange the equation by combining like terms: -8x + 6x ≤ 2 - 6.
Step 3: Simplify further: -2x ≤ -4.
Step 4: Divide both sides of the inequality by -2. Note that dividing an inequality by a negative number flips the inequality sign: x ≥ 2.
Therefore, all possible values of x that satisfy the inequality -8x + 6 ≤ 2(-3x + 1) are x values greater than or equal to 2.