Question

1) 3x-5=x+11. 2) (x-4)/3=(3x-5)/5-3. 3) |2x+6|=8.​

Answer 1

Ответ:

1)3x-x=11+5

2x=16.

2)5x-9x=-60+20

-4x=-40

x=10

3)2x+6=8

2x=2

x=1.

2x+6=-8

2x=-14

x=-7

Answer 2

Ответ:

1) 3x-5=x+11

3x-x=11+5

2x=16/:2

x=8

Ответ: 8

2) (x-4)/3=(3x-5)/5-3

x/3-4/3=(3x-5)/(5-3)

x/3-4/3=3x-55-3

-4/3+x/3=-5/2+3x/2

x/3=3x/2-7/6

(-7x)/6=-7/6/:7/6

x=1

Ответ: 1

3) |2x+6|=8

2x+6=8

2x=8-6

2x=2

x=1

(-2x-6)=8

-2x=8+6

-2x=14/:(-2)

x=-7

Ответ: 1; -7

Answer 3

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

1. 3x - 5 = x + 11

First, let's isolate x on one side of the equation. We can do this by subtracting x from both sides:

3x - x - 5 = x - x + 11

This simplifies to:

2x - 5 = 11

Now, let's add 5 to both sides to isolate 2x:

2x - 5 + 5 = 11 + 5

This simplifies to:

2x = 16

Now, divide both sides by 2 to solve for x:

(2x)/2 = 16/2

x = 8

So, the solution to the first equation is x = 8.

2. (x - 4)/3 = (3x - 5)/5 - 3

First, let's get rid of the fractions by multiplying both sides of the equation by the least common multiple of 3 and 5, which is 15. This will help simplify the equation:

15[(x - 4)/3] = 15[(3x - 5)/5] - 15(3)

Now, we can simplify the equation:

5(x - 4) = 3(3x - 5) - 45

Now, distribute on both sides of the equation:

5x - 20 = 9x - 15 - 45

Next, let's collect like terms by moving the 9x term to the left side of the equation and the constants to the right side:

5x - 9x = -15 - 45 + 20

This simplifies to:

-4x = -40

Now, divide both sides by -4 to solve for x:

(-4x)/(-4) = (-40)/(-4)

x = 10

So, the solution to the second equation is x = 10.

3. |2x + 6| = 8

To solve this equation, we'll consider two cases:

Case 1: 2x + 6 is positive or zero. In this case, the absolute value bars have no effect, so we have:

2x + 6 = 8

Now, subtract 6 from both sides:

2x = 8 - 6

2x = 2

Divide both sides by 2 to solve for x:

2x/2 = 2/2

x = 1

Case 2: 2x + 6 is negative. In this case, we need to negate 2x + 6 within the absolute value bars:

-(2x + 6) = 8

Now, subtract 6 from both sides:

-2x - 6 = 8

Add 6 to both sides:

-2x = 8 + 6

-2x = 14

Divide both sides by -2 to solve for x:

(-2x)/(-2) = 14/(-2)

x = -7

So, we have two solutions for the third equation: x = 1 and x = -7.