Question

Find the range of values of a, which satisfy 7 ≤ – 4x + 2 < 12, x ∈ R. Graph these values of a on the real number line.

Answer 1

7 ≤ – 4x + 2 < 12
7 < – 4x + 2 and – 4x + 2 < 12
4x ≤ 2 - 7 and -4x < 12 - 2
4x ≤ -5 and -4x < 10

`x ≤ (-5)/(4) and -x < (10)/(4)`

`x ≤ (-5)/(4) and -x < (5)/(4)`

or 
`x > -(5)/(2)`
∵ x ∈ R
∴ Solution set `-(5)/(2) < x ≤ (-5)/(2)`

= `{x : x ∈ "R", - (5)/(2) < x ≤ (-5)/(4)}`
Solution set on number line