Question

Solve −12 < `(4-3x)/-5 <2, x ∈ R` and represent the solution on the number line.

Answer 1

−12 < `(4-3x)/-5 <2, x ∈ R`

Multiply the entire inequality by −5

−12 < `(4-3x)/-5 <2`

⇒ ​60 > 4 − 3x > −10

−10 < 4 − 3x < 60

Subtract 4 from all parts

−10 − 4 < 4 − 3x − 4 < 60 − 4

⇒ −14 < −3x < 56

Divide by −3

`(-14)/-3 > x > 56/-3`

`(14)/3 > x > -56/3`

x ∈ `(-56/3, 14/3)`