Question

(4х-5)(6-3х)-4< (1-2х)(7х+6х)

Answer 1

24x-12-30+15x-4<7x+6x-14x-12x
24x+15x-7x-6x+14x+12x<12+30+4
52x<46|:52
x<1,1.
потом строишь график неравенств, и отмечаешь точки.
Я не знаю правильно ли сделала

Answer 2

To solve the inequality, we need to simplify the expressions on both sides and then find the solution for the variable (x) that satisfies the inequality.

Let's start by simplifying the expressions step by step:

1. Simplify the left side of the inequality: (4x - 5)(6 - 3x) - 4

Expand the expression: = 24x - 12x^2 - 30 + 15x - 4

Combine like terms: = -12x^2 + 39x - 34

2. Simplify the right side of the inequality: (1 - 2x)(7x + 6x)

Expand the expression: = 7x - 14x^2 + 6x - 12x^2

Combine like terms: = -26x^2 + 13x

Now, the original inequality becomes: -12x^2 + 39x - 34 < -26x^2 + 13x

Next, we'll move all the terms to one side of the inequality to set it to zero: -12x^2 + 39x - 34 + 26x^2 - 13x < 0

Combine like terms again: 14x^2 + 26x - 34 < 0

Now, to solve this quadratic inequality, we can use one of two methods: factoring or the quadratic formula. Let's use factoring:

Step 1: Set the inequality to zero by moving all terms to one side: 14x^2 + 26x - 34 < 0

Step 2: Factor the quadratic equation (or find its roots): 14x^2 + 26x - 34 = 0

Step 3: Factor the quadratic expression: 2(7x^2 + 13x - 17) = 0

Step 4: Solve for x by setting each factor to zero: 7x^2 + 13x - 17 = 0

Using the quadratic formula (or factoring), we find the solutions for x: x = (-13 ± √(13^2 - 4 * 7 * -17)) / 2 * 7 x = (-13 ± √(169 + 476)) / 14 x = (-13 ± √645) / 14

Step 5: Evaluate the inequality in different intervals: We have two critical points: x = (-13 + √645) / 14 and x = (-13 - √645) / 14. We'll test these intervals: (a) x < (-13 - √645) / 14, (b) (-13 - √645) / 14 < x < (-13 + √645) / 14, and (c) x > (-13 + √645) / 14.

Interval (a): Choose x = -1: 14(-1)^2 + 26(-1) - 34 = 14 - 26 - 34 = -46 < 0

Interval (b): Choose x = 0: 14(0)^2 + 26(0) - 34 = -34 < 0

Interval (c): Choose x = 1: 14(1)^2 + 26(1) - 34 = 6 > 0

Now, let's summarize the results: (a) x < (-13 - √645) / 14 → Satisfied (b) (-13 - √645) / 14 < x < (-13 + √645) / 14 → Satisfied (c) x > (-13 + √645) / 14 → Not satisfied

Therefore, the solution to the inequality is: x < (-13 - √645) / 14 or (-13 - √645) / 14 < x < (-13 + √645) / 14