Question

A)|3x-9|=6 b)|6-5x|=0​

Answer 1

Ответ:

|3x-9|=6

3x-9≥0

(3x-9)-6=0

3x-15=0

x₁=5

Решили 1 часть решаем 2

3x-9<0

(9-3x)-6=0

3-3x=0

x₂=1

Ответ

x₁=5 ; x₂=1

b)|6-5x|=0​

5x-6≥0

5x-6=0

x₁=$\frac{6}{5}$

Решаем 2 часть

6-5x=0

x₂=$\frac{6}{5}$

Ответ

x=$\frac{6}{5}$

Пошаговое объяснение:

Answer 2

Let's solve the equations step by step:

a) |3x - 9| = 6

To solve for x in this equation, we need to consider two cases:

Case 1: 3x - 9 = 6 Adding 9 to both sides: 3x = 6 + 9 3x = 15 Dividing both sides by 3: x = 15 / 3 x = 5

Case 2: -(3x - 9) = 6 Note that when you have a negative sign in front of the absolute value, you change the sign inside the absolute value: -(3x - 9) = 6 -3x + 9 = 6 Subtracting 9 from both sides: -3x = 6 - 9 -3x = -3 Dividing both sides by -3 (remember to flip the inequality sign because you divided by a negative number): x = -3 / -3 x = 1

So, there are two solutions to the equation |3x - 9| = 6: x = 5 and x = 1.

b) |6 - 5x| = 0

In this case, we have an absolute value equal to 0. This means that the expression inside the absolute value must also be equal to 0.

6 - 5x = 0

Now, let's solve for x:

Adding 5x to both sides:

6 = 5x

Dividing both sides by 5:

x = 6 / 5

So, the solution to the equation |6 - 5x| = 0 is x = 6/5.