Question

1)|x-2x|=4. 2)7=|3x+8| 3)|2x-9|=|3-x|

Answer 1

Решение задания смотри на фотографии

Answer 2

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

1. |x - 2x| = 4

First, simplify the expression inside the absolute value:

|x - 2x| = |(-1x)| = |(-1)x| = |(-1)|x| = |x| = x (since |a| = a when a is non-negative)

Now the equation becomes:

x = 4

2. 7 = |3x + 8|

To solve this equation, we need to consider two cases: one when the expression inside the absolute value is positive and the other when it is negative.

Case 1: 3x + 8 is positive: If 3x + 8 is positive, then the equation becomes:

7 = 3x + 8

Subtract 8 from both sides:

3x = -1

Now, divide both sides by 3:

x = -1/3

Case 2: 3x + 8 is negative: If 3x + 8 is negative, then the equation becomes:

7 = -(3x + 8)

First, remove the negative sign by multiplying both sides by -1:

-7 = 3x + 8

Now, subtract 8 from both sides:

-15 = 3x

Finally, divide both sides by 3:

x = -5

So, we have two possible solutions: x = -1/3 and x = -5.

3. |2x - 9| = |3 - x|

Again, we need to consider two cases for the expressions inside the absolute values.

Case 1: 2x - 9 is positive and 3 - x is positive: If 2x - 9 and 3 - x are both positive, then the equation becomes:

2x - 9 = 3 - x

Add x to both sides:

3x - 9 = 3

Add 9 to both sides:

3x = 12

Now, divide both sides by 3:

x = 4

Case 2: 2x - 9 is negative and 3 - x is negative: If 2x - 9 and 3 - x are both negative, then the equation becomes:

-(2x - 9) = -(3 - x)

First, remove the negative sign on both sides:

2x - 9 = x - 3

Subtract x from both sides:

x - 9 = -3

Add 9 to both sides:

x = 6

So, in this case, x = 6.

Now, we have two potential solutions: x = 4 and x = 6.

To summarize, the solutions for each equation are as follows:

1. x = 4
2. x = -1/3 or x = -5
3. x = 4 or x = 6