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

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)

a

step-by-step explanation:

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15