Question

2*x+4×7*x+4>2*3x×7*3x

Answer 1

2x+4•7x+4>2•3x•7•3x

2x+28x+4>6x•21x

30x+4>126x^2

-126x^2+30x+4=0

D=b-4ac=30-4•(-126•4)=2045

x1,2=

$\frac{ - b + - \sqrt{d} }{2a}$

x1=-2/21

x2=1/3

Answer 2

Let's simplify the inequality step by step to find the solution:

1. Distribute the multiplication: 2x + 47x + 4 > 23x73x

2. Perform the multiplications: 2x + 28x + 4 > 2*21x^2

3. Combine like terms on the left side of the inequality: 30x + 4 > 42x^2

Now, we have a quadratic inequality. To solve it, we need to set it equal to zero and find the critical points:

42x^2 - 30x - 4 = 0

To simplify further, divide the whole equation by 2:

21x^2 - 15x - 2 = 0

Now, we can use the quadratic formula to find the critical points:

x = [-(-15) ± √((-15)^2 - 4 * 21 * (-2))] / (2 * 21)

x = [15 ± √(225 + 168)] / 42

x = [15 ± √393] / 42

Now, we have two possible critical points:

1. x = (15 + √393) / 42
2. x = (15 - √393) / 42

Now, we can check the intervals determined by these critical points to determine the solution to the inequality.

Let's choose a value for x in each of the following intervals:

Interval 1: x < (15 - √393) / 42 Interval 2: (15 - √393) / 42 < x < (15 + √393) / 42 Interval 3: x > (15 + √393) / 42

For Interval 1, let's choose x = 0: 30 * 0 + 4 > 42 * 0^2 4 > 0 (True)

For Interval 2, let's choose x = 1: 30 * 1 + 4 > 42 * 1^2 34 > 42 (False)

For Interval 3, let's choose x = 2: 30 * 2 + 4 > 42 * 2^2 64 > 168 (False)

Based on the analysis of the inequalities in the intervals, the solution to the original inequality is:

(15 - √393) / 42 < x < (15 + √393) / 42