Question

|3x-6|+|2-4x|+|x-5|=7

Answer 1

Ответ:

х=8

Пошаговое объяснение:

х-4×1+|x-5|=7

x+|x-5|=7+4

x+|x-5|=11

x=8

Answer 2

To solve the absolute value equation |3x - 6| + |2 - 4x| + |x - 5| = 7, we need to consider different cases based on the sign of the expressions within the absolute value bars. Let's break down the equation into these cases and solve for x in each case:

Case 1: 3x - 6 is non-negative, 2 - 4x is non-negative, x - 5 is non-negative In this case, we can remove the absolute value bars without changing the sign:

3x - 6 + 2 - 4x + x - 5 = 7 Combine like terms: 0x - 9 = 7 This is not possible, so there are no solutions in this case.

Case 2: 3x - 6 is non-negative, 2 - 4x is non-negative, x - 5 is negative Here, we need to negate the expression inside the last absolute value:

3x - 6 + 2 - 4x - (x - 5) = 7 Simplify: 0x + 1 = 7 This leads to a contradiction, so there are no solutions in this case.

Case 3: 3x - 6 is non-negative, 2 - 4x is negative, x - 5 is non-negative Negate the expression inside the second absolute value:

3x - 6 - (2 - 4x) + x - 5 = 7 Simplify: 8x - 13 = 7 8x = 20 x = 2.5

Case 4: 3x - 6 is non-negative, 2 - 4x is negative, x - 5 is negative Negate both expressions inside the second and third absolute values:

3x - 6 - (2 - 4x) - (x - 5) = 7 Simplify: 6x + 1 = 7 6x = 6 x = 1

Case 5: 3x - 6 is negative, 2 - 4x is non-negative, x - 5 is non-negative Negate the expression inside the first absolute value:

-(3x - 6) + 2 - 4x + x - 5 = 7 Simplify: -3x + 4x - x = 20 0x = 20 This is not possible, so there are no solutions in this case.

Case 6: 3x - 6 is negative, 2 - 4x is non-negative, x - 5 is negative Negate both expressions inside the first and third absolute values:

-(3x - 6) + 2 - 4x - (x - 5) = 7 Simplify: -3x + 4x + x = 20 2x = 20 x = 10

Case 7: 3x - 6 is negative, 2 - 4x is negative, x - 5 is non-negative Negate the expression inside the first absolute value:

-(3x - 6) - (2 - 4x) + x - 5 = 7 Simplify: -3x + 4x - x = 20 0x = 20 This is not possible, so there are no solutions in this case.

Case 8: 3x - 6 is negative, 2 - 4x is negative, x - 5 is negative Negate all expressions inside the absolute values:

-(3x - 6) - (2 - 4x) - (x - 5) = 7 Simplify: -3x + 4x + x = 20 2x = 20 x = 10

After considering all cases, we have found two solutions: x = 2.5 and x = 10. These are the values of x that satisfy the original equation.