Question

1) 5 – 3(2х + 7) = 4(2 – х); 2) 3х(х – 1) – 17 = х(1 + 3х) + 1; 3) 2х – (х + 2)(2 – х) = 5 – (х – 1)2;

Answer 1

Ответ:

1)5-3(2х+7)=4(2-х)

5-6х-21=8-4х

-16-6х=8-4х

-16-8=-4х+6х

-24=2х

х= -24:2

х= -12

2)3х(х-1)-17=х(1+3х)+1

3х²-3х-17=х+3х²+1

3х²-3х-х-3х²=1+17

-4х=18

х= -(18:4)

х=4,5

3)2х-(х+2)(2-х)=5-(х-1)2

2х-х-2(2-х)=5-2х+2

2х-х-4+2х=5-2х+2

3х-4=7-2х

3х+2х=7+4

5х=11

х=11:5

х=2,2

Answer 2

Let's solve each of these equations step by step:

1. 5 - 3(2x + 7) = 4(2 - x)

First, distribute the numbers inside the parentheses:

5 - 6x - 21 = 8 - 4x

Now, combine like terms on both sides of the equation:

5 - 21 - 8 = -6x + 4x

-24 = -2x

Now, divide both sides by -2 to isolate x:

-24 / -2 = x

x = 12

So, the solution to the first equation is x = 12.

2. 3x(x - 1) - 17 = x(1 + 3x) + 1

First, distribute the numbers inside the parentheses:

3x^2 - 3x - 17 = x + 3x^2 + 1

Now, subtract x and 3x^2 from both sides of the equation to move all terms to one side:

3x^2 - 3x - 17 - x - 3x^2 - 1 = 0

Now, combine like terms:

-4x - 18 = 0

Next, add 18 to both sides of the equation:

-4x = 18

Now, divide both sides by -4 to isolate x:

-4x / -4 = 18 / -4

x = -4.5

So, the solution to the second equation is x = -4.5.

3. 2x - (x + 2)(2 - x) = 5 - (x - 1)^2

First, distribute the numbers inside the parentheses:

2x - (2x - x^2 + 2x - 2) = 5 - (x^2 - 2x + 1)

Now, simplify the expressions inside the parentheses:

2x - (2x - x^2 + 2x - 2) = 5 - x^2 + 2x - 1

Next, distribute the negative sign on the left side of the equation:

2x - 2x + x^2 - 2 = 5 - x^2 + 2x - 1

Now, combine like terms on both sides:

x^2 - 2 = 4 - x^2 + 2x

Add 2 to both sides:

x^2 + x - 2 = 4

Now, move all terms to one side:

x^2 + x - 2 - 4 = 0

x^2 + x - 6 = 0

Now, factor the quadratic equation:

(x + 3)(x - 2) = 0

Now, set each factor equal to zero and solve for x:

x + 3 = 0 or x - 2 = 0

x = -3 or x = 2

So, the solutions to the third equation are x = -3 and x = 2.