Question

Неравенство 1) -2x²-5x+3>0 2) -10≤3x-4<2

Answer 1

................................

Answer 2

To solve the inequalities, we need to find the ranges of values for the variable 'x' that satisfy each inequality. Let's solve them one by one:

1. -2x² - 5x + 3 > 0

Step 1: Factorize the quadratic expression on the left-hand side: -2x² - 5x + 3 = -(2x - 3)(x + 1)

Step 2: Find the critical points by setting each factor to zero and solving for 'x': (2x - 3) = 0 => 2x = 3 => x = 3/2 (x + 1) = 0 => x = -1

Step 3: Create a sign chart to check the sign of the expression in different intervals:

scssCopy code
       x < -1     -1 < x < 3/2     x > 3/2
       ---------|---------------|---------|---------
          (-)         (+)           (-)

Step 4: Determine the solution:

The inequality is satisfied when the expression is greater than zero, which is when it's positive (denoted by '+'). Therefore, the solution is: x < -1 or x > 3/2

2. -10 ≤ 3x - 4 < 2

Step 1: Solve the two separate inequalities:

-10 ≤ 3x - 4: Add 4 to both sides: -10 + 4 ≤ 3x -6 ≤ 3x Divide both sides by 3 (remembering to reverse the inequality when dividing by a negative number): -2 ≤ x

3x - 4 < 2: Add 4 to both sides: 3x < 6 Divide both sides by 3: x < 2

Step 2: Combine the results from the two inequalities: -2 ≤ x < 2

So, the solution to the second inequality is: -2 ≤ x < 2. This means 'x' can take any value within the range from -2 (inclusive) to 2 (exclusive).