Question

What's the inequality for |u|-2<5

Answer 1

0 ≤ u < 7 and 0 > u > - 7 and combining those two we get - 7 < u < 7.

Step-by-step explanation:

The given inequality is |u| - 2 < 5 ....... (1)

We have to solve this inequality.

Now, from the definition of f(x) = |x| we get, f(x) = x, when x ≥ 0 and

f(x) = -x when x < 0.

Hence, for u ≥ 0, the equation of inequality (1) becomes

u - 2 < 5

⇒ u < 7

Therefore, the solution is 0 ≤ u < 7 (Answer)

Again, for u < 0, the equation of inequality (1) becomes

- u - 2 < 5

⇒ u + 2 > - 5

⇒ u > - 7

Therefore, the solution becomes 0 > u > - 7 (Answer)