Question

1. |5x – 4| =10. 2. |2x – 6|+|x+2|+5= 0.3. |3x - 5| = x-1.4. |3x+2| = x+1.5. |3x + 2| = |2x - 3|.​

Answer 1

Пошаговое объяснение:

$1) 5x + 4 = 10\\5x = 10 - 4\\5x = 6\\x = \frac{6}{5} \\x = 1.2\\\\2)2x + 6 + x + 2 = 0\\2x + x = 0 - 6 - 2\\3x = -8\\x =-\frac{8}{3} \\\\3)3x + 5 = x-1\\3x - x = -1-5\\2x = -6\\x = \frac{-6}{2}\\x=-3\\\\\\4)3x+2=x+1\\3x-x=1-2\\2x = -1\\x = \frac{-1}{2}\\x = -0.5\\\\\\5)3x+2 = 2x+3\\3x - 2x = 3 - 2\\x = 1$

Answer 2

Let's solve each of these absolute value equations one by one:

1. |5x - 4| = 10

To solve this equation, you can split it into two cases:

Case 1: 5x - 4 = 10 5x = 14 x = 14/5

Case 2: -(5x - 4) = 10 -5x + 4 = 10 -5x = 10 - 4 -5x = 6 x = -6/5

So, the solutions are x = 14/5 and x = -6/5.

2. |2x - 6| + |x + 2| + 5 = 0

This equation has an absolute value on the left side, which represents a non-negative value. Therefore, it is impossible for the left side to equal 0. Therefore, there are no real solutions to this equation.

3. |3x - 5| = x - 1

Split the equation into two cases:

Case 1: 3x - 5 = x - 1 2x = 4 x = 2

Case 2: -(3x - 5) = x - 1 -3x + 5 = x - 1 -3x = x - 1 - 5 -3x = -6 x = 2

So, the solution is x = 2.

4. |3x + 2| = x + 1

Split the equation into two cases:

Case 1: 3x + 2 = x + 1 2x = -1 x = -1/2

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

So, the solutions are x = -1/2 and x = -3/4.

5. |3x + 2| = |2x - 3|

Split the equation into two cases:

Case 1: 3x + 2 = 2x - 3 x = -5

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

So, the solutions are x = -5 and x = 1/5.