Question

1)1-5x=-6x+8 2)-9(8-9x)=4x+5 3)x^2+3x=4 4)(x+10)^2=(5-x)^2

Answer 1

1) -5x+6x=-1+8

x=7

2) -72+81x=4x+5

81x-4x=72+5

77x=77

x=1

3) x^2+3x-4=0

x1*x2=-3

x1+x2=-4

x1=-1 ,x2=-3

4) x^2+20x+100=25-10x+x^2

30x=-75

x=-2.5

Answer 2

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

1. 1 - 5x = -6x + 8

First, we want to get the x terms on one side and the constants on the other side:

1 + 6x = 8 - 5x

Now, add 5x to both sides:

1 + 6x + 5x = 8

Combine like terms:

1 + 11x = 8

Subtract 1 from both sides:

11x = 8 - 1

11x = 7

Now, divide both sides by 11 to isolate x:

x = 7/11

2. -9(8 - 9x) = 4x + 5

First, distribute the -9 on the left side of the equation:

-72 + 81x = 4x + 5

Now, get the x terms on one side and the constants on the other side:

-72 - 5 = 4x - 81x

-77 = -77x

Now, divide both sides by -77 to isolate x:

x = (-77) / (-77)

x = 1

3. x^2 + 3x = 4

First, move 4 to the other side of the equation:

x^2 + 3x - 4 = 0

This is a quadratic equation. You can solve it by factoring or using the quadratic formula. In this case, let's factor it:

(x + 4)(x - 1) = 0

Now, set each factor equal to zero:

x + 4 = 0 or x - 1 = 0

For the first equation, subtract 4 from both sides:

x = -4

For the second equation, add 1 to both sides:

x = 1

So, the solutions are x = -4 and x = 1.

4. (x + 10)^2 = (5 - x)^2

First, expand both sides of the equation:

x^2 + 20x + 100 = 25 - 10x + x^2

Now, get the x terms on one side and the constants on the other side:

x^2 - x^2 + 20x + 10x = 25 - 100

Combine like terms:

30x = -75

Now, divide both sides by 30 to isolate x:

x = -75 / 30

Simplify the fraction:

x = -5/2

So, the solution is x = -5/2.