Question

Решить примеры: 1 - |0,2x−2|=3,6; 2 - |3−1,5x|=1,5; 3 - |15х−13,5|−7=2. Спасибо <33

Answer 1

$\displaystyle 1)|0,2x-2|=3,6\\0,2x-2=3,6;0,2x-2=-3,6\\x_{1}=-8,x_{2}=28\\\\ 2)|3-1,5x|=1,5\\3-1,5x=1,5;3-1,5x=-1,5\\x_{1}=1,x_{2}=3\\\\ 3)|15x-13,5|-7=2\\|15x-13,5|=2+7\\|15x-13,5|=9\\15x-13,5=9;15x-13,5=-9\\x_{1}=0,3;x_{2}=1,5$

Answer 2

Solution to the Equations:

Let's solve the given equations one by one:

1. Equation 1: |0.2x - 2| = 3.6

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

Case 1: 0.2x - 2 > 0 Solving for x: 0.2x - 2 = 3.6 0.2x = 5.6 x = 5.6 / 0.2 x = 28

Case 2: 0.2x - 2 < 0 Solving for x: -(0.2x - 2) = 3.6 -0.2x + 2 = 3.6 -0.2x = 1.6 x = 1.6 / -0.2 x = -8

Therefore, the solutions to the equation |0.2x - 2| = 3.6 are x = 28 and x = -8.

2. Equation 2: |3 - 1.5x| = 1.5

Again, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 3 - 1.5x > 0 Solving for x: 3 - 1.5x = 1.5 -1.5x = -1.5 x = -1.5 / -1.5 x = 1

Case 2: 3 - 1.5x < 0 Solving for x: -(3 - 1.5x) = 1.5 -3 + 1.5x = 1.5 1.5x = 4.5 x = 4.5 / 1.5 x = 3

Therefore, the solutions to the equation |3 - 1.5x| = 1.5 are x = 1 and x = 3.

3. Equation 3: |15x - 13.5| - 7 = 2

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

Case 1: 15x - 13.5 > 0 Solving for x: |15x - 13.5| - 7 = 2 15x - 13.5 - 7 = 2 15x - 20.5 = 2 15x = 22.5 x = 22.5 / 15 x = 1.5

Case 2: 15x - 13.5 < 0 Solving for x: |-(15x - 13.5)| - 7 = 2 -15x + 13.5 - 7 = 2 -15x + 6.5 = 2 -15x = -4.5 x = -4.5 / -15 x = 0.3

Therefore, the solutions to the equation |15x - 13.5| - 7 = 2 are x = 1.5 and x = 0.3.

So, the solutions to the given equations are: For Equation 1: x = 28, x = -8 For Equation 2: x = 1, x = 3 For Equation 3: x = 1.5, x = 0.3

I hope this helps! Let me know if you have any further questions.