Question

5)|10х-7|-32=50 6)||х|+10|=23

Answer 1

Пошаговое объяснение:

5 ) | 10х - 7 | - 32 = 50

| 10х - 7 | = 50 + 32

| 10х - 7 | = 82

10х - 7 = 82

10х - 7 = - 82

х = 89/ 10

х = - 15/2

х1 = - 15/2 = - 7,5

х2 = 89/10 = 8,9

6 ) | | х | + 10 | = 23

| х | + 10 = 23

| х | = 23 - 10

| х | = 13

х = 13

х = - 13

х1 = - 13

х2 = 13

Answer 2

To solve the equations, let's break them down one by one:

5. |10x - 7| - 32 = 50

First, we isolate the absolute value term:

|10x - 7| = 50 + 32 |10x - 7| = 82

Next, we split the equation into two cases, one where the expression inside the absolute value is positive and the other where it is negative:

Case 1: 10x - 7 > 0 If 10x - 7 is positive, then we can remove the absolute value signs:

10x - 7 = 82

Solving this equation:

10x = 82 + 7 10x = 89 x = 89/10 x = 8.9

Case 2: 10x - 7 < 0 If 10x - 7 is negative, we remove the absolute value signs and flip the inequality:

-(10x - 7) = 82

Solving this equation:

-10x + 7 = 82 -10x = 82 - 7 -10x = 75 x = 75/-10 x = -7.5

So the solutions to the equation |10x - 7| - 32 = 50 are x = 8.9 and x = -7.5.

6. |x| + 10 = 23

Isolate the absolute value term:

|x| = 23 - 10 |x| = 13

Again, split the equation into two cases:

Case 1: x > 0 If x is positive, we can remove the absolute value signs:

x = 13

Case 2: x < 0 If x is negative, we remove the absolute value signs and flip the inequality:

-x = 13

Solving this equation:

x = -13

So the solutions to the equation |x| + 10 = 23 are x = 13 and x = -13.