Question

|x|+3=5 , |y|-2=1, |x+3|=0, |x-5|=0

Answer 1

Ответ:

Пошаговое объяснение:

1) |х| + 3 = 5

|х| = 2

x = ±2

2) |y| - 2 = 1

|y| = 3

y = ±3

3) x + 3 = 0 при х + 3 >= 0

x = -3

-(x + 3) = 0 при х + 3 < 0

-x - 3 = 0

x = -3

4) x - 5 = 0 при х - 5 >= 0

x = 5

-(x - 5) = 0 при х - 5 < 0

-x + 5 = 0

x = 5

Answer 2

To solve the given equations, let's analyze them one by one:

Equation 1: |x| + 3 = 5

To eliminate the absolute value, we can split the equation into two cases:

Case 1: x ≥ 0 If x ≥ 0, then |x| = x. Substituting this into the equation, we have: x + 3 = 5 Solving for x: x = 5 - 3 x = 2

Case 2: x < 0 If x < 0, then |x| = -x. Substituting this into the equation, we have: -x + 3 = 5 Solving for x: -x = 5 - 3 -x = 2 Multiply both sides by -1 to get rid of the negative sign: x = -2

So the solutions for Equation 1 are x = 2 and x = -2.

Equation 2: |y| - 2 = 1

Adding 2 to both sides of the equation, we have: |y| = 3

To eliminate the absolute value, we can split the equation into two cases:

Case 1: y ≥ 0 If y ≥ 0, then |y| = y. Substituting this into the equation, we have: y = 3

Case 2: y < 0 If y < 0, then |y| = -y. Substituting this into the equation, we have: -y = 3 Multiply both sides by -1 to get rid of the negative sign: y = -3

So the solutions for Equation 2 are y = 3 and y = -3.

Equation 3: |x + 3| = 0

The absolute value of any number is always non-negative, so the only way for it to be equal to zero is if the expression inside the absolute value is also zero. Thus: x + 3 = 0 Solving for x: x = -3

So the solution for Equation 3 is x = -3.

Equation 4: |x - 5| = 0

Similar to Equation 3, the absolute value of any number is only equal to zero when the expression inside the absolute value is zero. Thus: x - 5 = 0 Solving for x: x = 5

So the solution for Equation 4 is x = 5.

In summary, the solutions for the given equations are: Equation 1: x = 2, x = -2 Equation 2: y = 3, y = -3 Equation 3: x = -3 Equation 4: x = 5