Question

| х ÷ 5 | = 8/9 × | 4/5 - 7/8 |​

Answer 1

Ответ:

x1=-1/3   x2=1/3

Пошаговое объяснение:

|1/5x|=8/9*|-3/40|

1/5*|x|=8/9*3/40

1/5*|x|=1/3*1/5

1/5*|x|=1/15

|x|=1/3

x1=-1/3   x2=1/3

Answer 2

To solve the equation |x ÷ 5| = (8/9) × |(4/5) - (7/8)|, you can follow these steps:

1. Calculate the absolute value of the difference inside the second absolute value:

   |(4/5) - (7/8)|

   To subtract fractions, you need a common denominator, which is 40 in this case. So:

   |(32/40) - (35/40)| = |(32 - 35)/40| = |(-3)/40|

   Now, you have |(-3)/40|.

2. Calculate the right side of the equation:

   (8/9) × |(-3)/40|

   To multiply fractions, you simply multiply the numerators and denominators:

   (8/9) × (|-3|/40) = (8/9) × (3/40)

   Now, you have (8/9) × (3/40).

3. Simplify the right side of the equation further:

   (8/9) × (3/40) = (8/9) × (3/8) × (1/5)

   You can simplify (3/8) by dividing both the numerator and denominator by 4:

   (8/9) × (3/8) × (1/5) = (1/3) × (1/5)

   Now, you have (1/3) × (1/5).

4. Multiply the fractions on the right side:

   (1/3) × (1/5) = 1/15

Now, you have simplified the right side of the equation to 1/15:

|x ÷ 5| = 1/15

5. To solve for x, consider two cases for the absolute value:

   a. x ÷ 5 = 1/15 b. x ÷ 5 = -1/15

For the first case:

a. x ÷ 5 = 1/15

Multiply both sides by 5 to isolate x:

x = (1/15) × 5

x = 1/3

For the second case:

b. x ÷ 5 = -1/15

Multiply both sides by 5 to isolate x:

x = (-1/15) × 5

x = -1/3

So, the solutions to the equation are:

x = 1/3 and x = -1/3.