Question

Use the inequality to answer Parts 1-3.

Answer 1

Answer:

1. Incomplete

2. 8≥ 3 x + 5

⇒8-5≥3 x

⇒ 3 ≥ 3 x

Dividing both sides by 3

1≤ x or x ≥ 1 is the solution of above inequality.i.e x∈[1,0).

The solution of the above inequality is that x lies in the interval from 0 to 1 represented as 0≤x<1.

3.  -2 x + 3 > 3(2 x - 1)

⇒ -2 x + 3> 3× 2 x - 3× 1 ⇒ [using distributive property which is a(b+c)=a×b + a× c]

⇒-2 x - 6 x > -3-3 →[ Bringing like terms together]

⇒ - 8 x > -6

Cancelling negative sign from both sides

if ,-a>-b, then a<b.

⇒8 x< 6

⇒x<6/8

⇒x<3/4

x∈(-∞,3/4)

The solution of the above inequality is x should be less than three by four.