Final Answer:
The solution to the inequality 6x²-14x≥-4 is x ≤ 1/3 or x ≥ 2. Option A is answer.
Explanation:
To solve the inequality 6x²-14x≥-4, we can start by adding 4 to both sides of the inequality:
6x²-14x+4 ≥ 0
Next, we can simplify the left-hand side of the inequality by factoring out a 2:
2(3x²-7x+2) ≥ 0
Now we can factor the quadratic expression inside the parentheses:
2(3x-1)(x-2) ≥ 0
The inequality is satisfied when the expression on the left-hand side is greater than or equal to zero. We can use a sign chart to determine the values of x that satisfy the inequality:
Interval 3x-1 x-2 2(3x-1)(x-2)
x < 1/3 - - +
1/3 < x < 2 + - -
x > 2 + + +
Therefore, the solution to the inequality 6x²-14x≥-4 is x ≤ 1/3 or x ≥ 2 . Option A is answer.