Question

|x-4|=2; |y+5|=3; |3+x|=1,5; |7-у|=-2; |х+3|+4=9; |у-2|+8=5 Заранее спасибо!! Огромное

Answer 1

| x-4 | = 2;
x-4 = 2 и x-4 = -2
x = 6 и x = 2
Ответ: 6; 2.

| y+5| = 3
y+5 = 3 и y+5 = -3
y=-2 и y = -8
Ответ: -2; -8

|3+x| = 1.5
3+x = 1.5 и 3+x = -1.5
x = -1.5 и x = -4.5
Ответ: -1.5; -4,5

|7-у| = -2
7-y = -2 и 7-y = 2
y = 9 и y = -5
Ответ: 9; -5

|х+3|+4 = 9
|x+3| = 9-4
|x+3| = 5
x+3 = 5 и x+3 = -5
x = 2 и x = -8
Ответ: 2; -8

|у-2|+8=5
|y-2| = 5-8
|y-2| = -3
y-2 = -3 и y-2 = 3
y = -1 и y = 5
Ответ: -1; 5

Answer 2

Equation 1: |x-4|=2

To solve the equation |x-4|=2, we need to consider two cases: when x-4 is positive and when x-4 is negative.

Case 1: x-4 is positive In this case, we have x-4=2. Adding 4 to both sides of the equation, we get x=6.

Case 2: x-4 is negative In this case, we have -(x-4)=2. Simplifying the equation, we get -x+4=2. Subtracting 4 from both sides of the equation, we get -x=-2. Multiplying both sides by -1, we get x=2.

Therefore, the solutions to the equation |x-4|=2 are x=6 and x=2.

Equation 2: |y+5|=3

To solve the equation |y+5|=3, we also need to consider two cases: when y+5 is positive and when y+5 is negative.

Case 1: y+5 is positive In this case, we have y+5=3. Subtracting 5 from both sides of the equation, we get y=-2.

Case 2: y+5 is negative In this case, we have -(y+5)=3. Simplifying the equation, we get -y-5=3. Adding 5 to both sides of the equation, we get -y=8. Multiplying both sides by -1, we get y=-8.

Therefore, the solutions to the equation |y+5|=3 are y=-2 and y=-8.

Equation 3: |3+x|=1.5

To solve the equation |3+x|=1.5, we again consider two cases: when 3+x is positive and when 3+x is negative.

Case 1: 3+x is positive In this case, we have 3+x=1.5. Subtracting 3 from both sides of the equation, we get x=-1.5.

Case 2: 3+x is negative In this case, we have -(3+x)=1.5. Simplifying the equation, we get -3-x=1.5. Adding 3 to both sides of the equation, we get -x=4.5. Multiplying both sides by -1, we get x=-4.5.

Therefore, the solutions to the equation |3+x|=1.5 are x=-1.5 and x=-4.5.

Equation 4: |7-y|=-2

The equation |7-y|=-2 has no solutions. The absolute value of any number is always non-negative, so it cannot be equal to a negative number.

Equation 5: |x+3|+4=9

To solve the equation |x+3|+4=9, we need to isolate the absolute value term.

Subtracting 4 from both sides of the equation, we get |x+3|=5.

Again, we consider two cases: when x+3 is positive and when x+3 is negative.

Case 1: x+3 is positive In this case, we have x+3=5. Subtracting 3 from both sides of the equation, we get x=2.

Case 2: x+3 is negative In this case, we have -(x+3)=5. Simplifying the equation, we get -x-3=5. Adding 3 to both sides of the equation, we get -x=8. Multiplying both sides by -1, we get x=-8.

Therefore, the solutions to the equation |x+3|+4=9 are x=2 and x=-8.

Equation 6: |y-2|+8=5

To solve the equation |y-2|+8=5, we isolate the absolute value term.

Subtracting 8 from both sides of the equation, we get |y-2|=-3.

The absolute value of any number is always non-negative, so it cannot be equal to a negative number. Therefore, the equation has no solutions.

In summary, the solutions to the given equations are as follows: - Equation 1: x=6 and x=2 - Equation 2: y=-2 and y=-8 - Equation 3: x=-1.5 and x=-4.5 - Equation 4: No solutions - Equation 5: x=2 and x=-8 - Equation 6: No solutions