Question

1) |6-4х|=22) |х+2|-3=8-|2х+4|​

Answer 1

Ответы на картинке с объяснением

Answer 2

Let's solve the equations one by one:

1. |6-4x| = 22

To solve this equation, we need to consider two cases: one where the expression inside the absolute value is positive, and another where it is negative.

Case 1: 6 - 4x is positive In this case, the absolute value simplifies to the expression inside it. 6 - 4x = 22 Subtract 6 from both sides: -4x = 16 Divide both sides by -4: x = -4

Case 2: 6 - 4x is negative In this case, the absolute value becomes the negation of the expression inside it. -(6 - 4x) = 22 Distribute the negative sign: -6 + 4x = 22 Add 6 to both sides: 4x = 28 Divide both sides by 4: x = 7

So the solutions to the equation |6-4x| = 22 are x = -4 and x = 7.

2. |x+2| - 3 = 8 - |2x+4|

Similar to the first equation, we'll consider different cases based on the expressions inside the absolute values.

Case 1: x + 2 is positive and 2x + 4 is positive In this case, both absolute values simplify to the expressions inside them. x + 2 - 3 = 8 - (2x + 4) Combine like terms: x - 1 = 8 - 2x - 4 Combine like terms again: x + 2x = 8 - 4 + 1 3x = 5 Divide both sides by 3: x = 5/3

Case 2: x + 2 is positive and 2x + 4 is negative In this case, the absolute value of 2x + 4 becomes the negation of the expression inside it. x + 2 - 3 = 8 + (2x + 4) x - 1 = 8 + 2x + 4 x - 1 = 12 + 2x Subtract x from both sides: -1 = 12 + x Subtract 12 from both sides: x = -13

Case 3: x + 2 is negative and 2x + 4 is positive In this case, the absolute value of x + 2 becomes the negation of the expression inside it. -(x + 2) - 3 = 8 - (2x + 4) -x - 2 - 3 = 8 - 2x - 4 -x - 5 = 4 - 2x Add x to both sides: -5 = 4 - x Subtract 4 from both sides: -9 = -x Multiply both sides by -1: 9 = x

Case 4: x + 2 is negative and 2x + 4 is negative In this case, both absolute values become the negation of the expressions inside them. -(x + 2) - 3 = 8 + (2x + 4) -x - 2 - 3 = 8 + 2x + 4 -x - 5 = 12 + 2x Add x to both sides: -5 = 12 + 3x Subtract 12 from both sides: -17 = 3x Divide both sides by 3: x = -17/3

So the solutions to the equation |x+2|-3 = 8-|2x+4| are x = 5/3, x = -13, x = 9, and x = -17/3.