Question

Consider the following inequality:3-2 < = +4412+ 4Step 1 of 2: Write the solution using interval notation.

Answer 1

(- ∞, 4)

Explanation:

`(3)/(4)z-2\: < \:-(3)/(4)z\:+\:4`

Add 2 to both sides:

`(3)/(4)z-2+2 < -(3)/(4)z+4+2`

`\rightarrow (3)/(4)z < -(3)/(4)z+6`

Add
`(3)/(4)z` to both sides

`(3)/(4)z+(3)/(4)z < -(3)/(4)z+6+(3)/(4)z`

`(3)/(2)z < 6\\\\\\`

`\rightarrow z < 6 \cdot (2)/(3)\\\\z < 4`

There is no lower limit on z so we get the soluton as

-∞ < z < 4

which in interval notation is

(-∞ , 4)