Question

Решите уравнения 1) |m+8| = 2 2) |m-9| = 5 3) |n-7| = 2 4) |15+n| = 3 пж

Answer 1

Пошаговое объяснение:

1) |m+8| = 2

m+8=2

m=2-8

m₁=-6

m+8=-2

m=-2-8

m₂=-10

2) |m-9| = 5

m-9=5

m=5+9

m₁=14

m-9=-5

m=-5+9

m₂=4

3) |n-7| = 2

n-7=2

n=7+2

n₁=9

n-7=-2

n=7-2

n₂=5

4) |15+n| = 3

15+n=3

n=3-15

n₁=-12

15+n=-3

n=-3-15

n₂=-18

Answer 2

1. |m + 8| = 2:

To solve this equation, we need to consider two cases: when m + 8 is positive and when it is negative.

Case 1: m + 8 is positive. If m + 8 is positive, we have: m + 8 = 2 m = 2 - 8 m = -6

Case 2: m + 8 is negative. If m + 8 is negative, we have: -(m + 8) = 2 -m - 8 = 2 -m = 2 + 8 -m = 10 m = -10

So, the solutions to the equation |m + 8| = 2 are m = -6 and m = -10.

2. |m - 9| = 5:

Again, we need to consider two cases: when m - 9 is positive and when it is negative.

Case 1: m - 9 is positive. If m - 9 is positive, we have: m - 9 = 5 m = 5 + 9 m = 14

Case 2: m - 9 is negative. If m - 9 is negative, we have: -(m - 9) = 5 -m + 9 = 5 -m = 5 - 9 -m = -4 m = 4

So, the solutions to the equation |m - 9| = 5 are m = 14 and m = 4.

3. |n - 7| = 2:

Again, we consider two cases: when n - 7 is positive and when it is negative.

Case 1: n - 7 is positive. If n - 7 is positive, we have: n - 7 = 2 n = 2 + 7 n = 9

Case 2: n - 7 is negative. If n - 7 is negative, we have: -(n - 7) = 2 -n + 7 = 2 -n = 2 - 7 -n = -5 n = 5

So, the solutions to the equation |n - 7| = 2 are n = 9 and n = 5.

4. |15 + n| = 3:

Again, we consider two cases: when 15 + n is positive and when it is negative.

Case 1: 15 + n is positive. If 15 + n is positive, we have: 15 + n = 3 n = 3 - 15 n = -12

Case 2: 15 + n is negative. If 15 + n is negative, we have: -(15 + n) = 3 -15 - n = 3 -n = 3 + 15 -n = 18 n = -18

So, the solutions to the equation |15 + n| = 3 are n = -12 and n = -18.