Question

|5y|-4=6 4+|3y|=7|x-5|=0|2-x|=0|9+x|-0,7=-0,7​

Answer 1

Ответ:

1)5y=10

y=2

2)3y=3

y=1

3)x=5

4)-x=-2

x=2

5)9+x=0

x=-9

Answer 2

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

1. |5y| - 4 = 6

First, add 4 to both sides of the equation:

|5y| - 4 + 4 = 6 + 4

|5y| = 10

Now, you have an absolute value equation. Remember that the absolute value of a number can be positive or negative, so you need to consider both cases:

Case 1: 5y = 10

Now, divide both sides by 5:

5y/5 = 10/5

y = 2

Case 2: -5y = 10

Divide both sides by -5 (and remember that when you divide by a negative number, the inequality sign flips):

-5y/(-5) = 10/(-5)

y = -2

So, the solutions to the equation |5y| - 4 = 6 are y = 2 and y = -2.

2. 4 + |3y| = 7

First, subtract 4 from both sides of the equation:

4 + |3y| - 4 = 7 - 4

|3y| = 3

Now, like in the previous equation, consider both cases for the absolute value:

Case 1: 3y = 3

Divide both sides by 3:

3y/3 = 3/3

y = 1

Case 2: -3y = 3

Divide both sides by -3 (and remember to flip the inequality sign):

-3y/(-3) = 3/(-3)

y = -1

So, the solutions to the equation 4 + |3y| = 7 are y = 1 and y = -1.

3. |x - 5| = 0

The absolute value of any real number is always non-negative. Therefore, the absolute value can only be equal to 0 when the expression inside it is equal to 0:

x - 5 = 0

Now, add 5 to both sides of the equation:

x - 5 + 5 = 0 + 5

x = 5

So, the only solution to the equation |x - 5| = 0 is x = 5.

4. |2 - x| = 0

Similar to the previous equation, the absolute value can only be equal to 0 when the expression inside it is equal to 0:

2 - x = 0

Now, subtract 2 from both sides of the equation:

2 - x - 2 = 0 - 2

-x = -2

Multiply both sides by -1 (and remember to flip the inequality sign):

-x * (-1) = -2 * (-1)

x = 2

So, the only solution to the equation |2 - x| = 0 is x = 2.

5. |9 + x| - 0.7 = -0.7

Add 0.7 to both sides of the equation:

|9 + x| - 0.7 + 0.7 = -0.7 + 0.7

|9 + x| = 0

Similar to the previous absolute value equations, the absolute value can only be equal to 0 when the expression inside it is equal to 0:

9 + x = 0

Now, subtract 9 from both sides of the equation:

9 + x - 9 = 0 - 9

x = -9

So, the solution to the equation |9 + x| - 0.7 = -0.7 is x = -9.