Question

0, 8(9 + 2x) = 0, 5(2 - 3x) ; 3(2x + 8) - (5x + 2) = 0 ; x - (2x + 3)/2 = (x - 1)/4 |2x - 3| = 5 ; |(x - 3)/2 + 5| = 4

Answer 1

Объяснение:

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Answer 2

It looks like you've provided a series of equations and expressions involving the variable "x." I'll solve each one step by step:

1. 0 = 8(9 + 2x) and 0 = 5(2 - 3x):

   First, let's solve the first equation:

   0 = 8(9 + 2x)

   Divide both sides by 8:

   0 = 9 + 2x

   Subtract 9 from both sides:

   -9 = 2x

   Divide by 2:

   -4.5 = x

   Now, let's solve the second equation:

   0 = 5(2 - 3x)

   Divide both sides by 5:

   0 = 2 - 3x

   Subtract 2 from both sides:

   -2 = -3x

   Divide by -3:

   2/3 = x

2. 3(2x + 8) - (5x + 2) = 0:

   First, distribute the 3 on the left side:

   6x + 24 - (5x + 2) = 0

   Now, remove the parentheses:

   6x + 24 - 5x - 2 = 0

   Combine like terms:

   6x - 5x + 24 - 2 = 0

   x + 22 = 0

   Subtract 22 from both sides:

   x = -22

3. x - (2x + 3)/2 = (x - 1)/4:

   Let's first get rid of the fractions by multiplying both sides by 4 (the least common multiple of 2 and 4):

   4x - 2(x + 3) = x - 1

   Now, distribute the -2 on the left side:

   4x - 2x - 6 = x - 1

   Combine like terms:

   2x - 6 = x - 1

   Subtract x from both sides:

   x - 6 = -1

   Add 6 to both sides:

   x = 5

4. |2x - 3| = 5:

   We'll consider two cases, one with the absolute value equal to 5, and one with it equal to -5 (which becomes 5 after taking the absolute value).

   Case 1: 2x - 3 = 5

   Add 3 to both sides:

   2x = 8

   Divide by 2:

   x = 4

   Case 2: 2x - 3 = -5

   Add 3 to both sides:

   2x = -2

   Divide by 2:

   x = -1

   So, there are two solutions: x = 4 and x = -1.

5. |(x - 3)/2 + 5| = 4:

   We'll consider two cases again.

   Case 1: (x - 3)/2 + 5 = 4

   Subtract 5 from both sides:

   (x - 3)/2 = -1

   Multiply both sides by 2:

   x - 3 = -2

   Add 3 to both sides:

   x = 1

   Case 2: -(x - 3)/2 - 5 = 4

   Add 5 to both sides:

   -(x - 3)/2 = 9

   Multiply both sides by -2:

   x - 3 = -18

   Add 3 to both sides:

   x = -15

   So, there are two solutions: x = 1 and x = -15.

These are the solutions for each equation and expression.