Question

ДАЮ 25 БАЛОВ 1.x-5/3-x-7/4-5=x/3 2.(2x-3)²-(5-2x)²+7(x-3)=20 3.5x(x-3)-x(4+5x)=2(3x-8) 4.(3x-2)(4x+3)-(4+7)(9+3x)=5x+3

Answer 1

1) -5/3-7/4-5=x/3

-5-21/4-15=x

x=-20-5-1/4=-(25+1/4)

2) 4x^2-12x+9-25+20x-4x^2+7x-21=20

15x=20+21+16

x=57/15=19/5

3) 5x^2-15x-4x-5x^2=6x-16

-19x=6x-16

16=25x

x=16/25

4) (3x-2)(4x+3)-(4x+7)(9+3x)=5x+3

12x^2+x-6-12x^2-57x-63=5x+3

-56x-69=5x+3

-72=61x

x=-72/61

Answer 2

To solve each of the given equations, let's go through them one by one:

1. x - 5/3 - x - 7/4 - 5 = x/3

Step 1: Combine like terms on the left side: -x - x - 5/3 - 7/4 - 5 = x/3

Step 2: Convert the fractions to a common denominator: (-4x - 7 - 35 - 60) / 12 = x/3

Step 3: Combine the constants on the left side: (-4x - 102) / 12 = x/3

Step 4: Cross-multiply: 3(-4x - 102) = 12x

Step 5: Distribute and simplify: -12x - 306 = 12x

Step 6: Move the variable terms to one side and constants to the other side: -12x - 12x = 306

Step 7: Combine the variable terms: -24x = 306

Step 8: Solve for x: x = 306 / -24 x = -51/4

2. (2x-3)² - (5-2x)² + 7(x-3) = 20

Step 1: Expand the squares: (4x² - 12x + 9) - (25 - 20x + 4x²) + 7x - 21 = 20

Step 2: Combine like terms: 4x² - 12x + 9 - 25 + 20x - 4x² + 7x - 21 = 20

Step 3: Simplify: -5x - 27 = 20

Step 4: Move the constant to the other side: -5x = 47

Step 5: Solve for x: x = 47 / -5 x = -47/5

3. 5x(x-3) - x(4+5x) = 2(3x-8)

Step 1: Distribute on both sides: 5x² - 15x - 4x - 5x² = 6x - 16

Step 2: Combine like terms: -19x = 6x - 16

Step 3: Move the variable terms to one side and constants to the other side: -19x - 6x = -16

Step 4: Combine the variable terms: -25x = -16

Step 5: Solve for x: x = -16 / -25 x = 16/25

4. (3x-2)(4x+3) - (4+7)(9+3x) = 5x+3

Step 1: Expand the expressions: 12x² + 9x - 8x - 6 - 63 - 21x = 5x + 3

Step 2: Combine like terms: 12x² + 9x - 8x - 6 - 63 - 21x - 5x - 3 = 0

Step 3: Simplify: 12x² - 25x - 72 = 0

Now, the equation is a quadratic equation, and we can solve it using the quadratic formula or factoring. Let's use factoring:

Step 4: Factor the quadratic equation: (3x + 8)(4x - 9) = 0

Step 5: Set each factor to zero and solve for x: 3x + 8 = 0 --> 3x = -8 --> x = -8 / 3

4x - 9 = 0 --> 4x = 9 --> x = 9 / 4

So, the solutions to the fourth equation are x = -8/3 and x = 9/4.