Question

1)5x+1=3x+1 2)6x-1=11 3)x-1=7(x-1) 4)x-2=1+4x 5)5x+5=(x-1)

Answer 1

1)5х+1=3х+1
5х-3х=1-1
2х=0
х=0:2
х=0

2)6х-1=11
6х=11+1
6х=12
х=12:6
х=2

3)х-1=7(х-1)
х-1=7х-7
х-7х=-7+1
-6х=-6
х=-6:(-6)
х=1

4)х-2=1+4х
х-4х=1+2
-3х=3
х=3:(-3)
х=-1

5)5х+5=(х-1)
5х-х=-1-5
4х=-6
х=-6:4
х=-1,5

Answer 2

Let's solve the given equations one by one:

1. 5x + 1 = 3x + 1 To solve this equation, we want to isolate the variable x. We can start by subtracting 3x from both sides: 5x - 3x + 1 = 3x - 3x + 1 2x + 1 = 1 Next, we can subtract 1 from both sides to isolate the term with x: 2x + 1 - 1 = 1 - 1 2x = 0 Finally, we divide both sides by 2 to solve for x: 2x/2 = 0/2 x = 0

So, the solution to the equation is x = 0.

2. 6x - 1 = 11 To solve this equation, we want to isolate the variable x. We can start by adding 1 to both sides: 6x - 1 + 1 = 11 + 1 6x = 12 Next, we divide both sides by 6 to solve for x: 6x/6 = 12/6 x = 2

So, the solution to the equation is x = 2.

3. x - 1 = 7(x - 1) This equation has a common term, (x - 1), on both sides. We can simplify the equation by dividing both sides by (x - 1): (x - 1)/(x - 1) = 7(x - 1)/(x - 1) 1 = 7

This equation is not true for any value of x. Therefore, it has no solution.

4. x - 2 = 1 + 4x To solve this equation, we want to isolate the variable x. We can start by subtracting x from both sides: x - 2 - x = 1 + 4x - x -2 = 1 + 3x Next, we can subtract 1 from both sides: -2 - 1 = 1 + 3x - 1 -3 = 3x Finally, we divide both sides by 3 to solve for x: -3/3 = 3x/3 -1 = x

So, the solution to the equation is x = -1.

5. 5x + 5 = x - 1 To solve this equation, we want to isolate the variable x. We can start by subtracting x from both sides: 5x - x + 5 = x - x - 1 4x + 5 = -1 Next, we can subtract 5 from both sides: 4x + 5 - 5 = -1 - 5 4x = -6 Finally, we divide both sides by 4 to solve for x: 4x/4 = -6/4 x = -3/2 or -1.5

So, the solution to the equation is x = -3/2 or x = -1.5.