To find the value of × that is in the solution set of the inequality 3x(x-4) > 5x + 2, we need to solve the inequality and identify the values of × that satisfy it. Step 1: Expand and simplify the left side of the inequality: 3x(x-4) = 3×^2 - 12x Step 2: Rewrite the inequality with the simplified expression: 3x^2 - 12x > 5x + 2 Step
3: Move all the terms to one side of the inequality by subtracting 5x and 2 from both sides: 3x^2 - 17x - 2 > 0 Step 4: Now we have a quadratic inequality. To solve it, we need to factor or use the quadratic formula. Step 5:
Factoring the quadratic expression, we have:
(3x + 1) (x - 2) > 0 Step 6: To determine the values of x that satisfy the inequality, we need to consider the signs of each factor. Step 7:
Setting each factor equal to zero and solving,
we find: 3x + 1 = 0 => x = -1/3 x - 2 = 0 => x = 2
Step 8: Now we can create a sign chart to determine the solution set: -0 -1/3 2 +00 (+) (-)
(+) (+) Step 9: From the sign chart, we can see that the inequality is satisfied when x is in the intervals (-∞, -1/3) and (2, +∞). Therefore, the solution set for the inequality 3x(x-4) > 5x + 2 is: (-00, -1/3) U (2, +∞). In conclusion, any value of x that is less than -1/3 or greater than 2 will make the inequality 3x(x-4) > 5x + 2 true.