# math inequality.Solve the inequality 5*|7n-7|<35.

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We have to solve : 5*|7n-7|<35

5*|7n-7|<35

=>|7n-7|<7

=> 7*|n - 1| < 7

=> |n - 1| < 1

=> -1 < (n - 1) < 1

-1 < (n - 1)

=> 0< n

(n - 1) < 1

=> n < 2

**The values of n lie in the interval (0, 2)**

The absolute value of a number |x| is equal to x if x>= 0 and -x if x < 0.

For the inequality 5*|7n-7|<35 first divide both sides by 5, |7n - 7| < 7

Now assume 7n - 7 >= 0 or n >= 1

7n - 7 < 7

7n < 14

n < 2

This gives the interval [1, 2)

Assume 7n - 7 < 0 or n < 1

7 - 7n < 7

0 < 7n

0 < n

This gives the interval (0, 1)

The solution of the given inequality is (0, 1)U([1, 12/7)

5*|7n-7|<35 <=> |7n-7|<7

Now, we'll discuss the absolute value of the expression 7n-7:

1) 7n-7for 7n-7>=0

7n>=7

n>=1

We'll solve the inequality:

7n-7 < 7

7n < 14

n < 14/7

n < 2

The interval of admissisble value of n, in this case, is [1, 2).

2) 7 - 7n, for 7n-7<0

7n<7

n<1

We'll solve the inequality:

7 - 7n< 7

-7n < 0

7n > 0

n > 0

The interval of admissible values for n, in this case, is (0 , 1).