Question

Write the following set as an interval: {x ∈ R ∶ − 1 3 < 2 − 7x ≤ 3 5 }
PLS HELP

Answer 1

Answer:

Given: −

3

x

≤

2

x

−1

3

1

<

6

1

Taking L.C.M. of 3,2 and 6 is 6.

−

3

x

×6≤

2

x

×6−

3

4

×6<

6

1

×6

−2x≤3x−8<1

⇒−2x≤3x−8 and 3x−8<1

⇒8≤3x+2x ⇒3x<1+8

⇒8≤5x ⇒3x<9

⇒

5

8

≤x ⇒x<3

∴ The solution set is {x:1.6≤x≤3,xϵR}