Question

How do you solve `12+ 4x \geq 22`?

Answer 1

`x>=5/2`

Explanation:

`"subtract 12 from both sides of the inequality"`

`rArr4x>=10`

`"divide both sides by 4"`

`rArrx>=10/4rArrx>=5/2" is the solution"`

`x in[5/2,oo)larrcolor(blue)"in interval notation"`

Answer 2

`x >= 5/2`

Explanation:

`12 + 4x >= 22`

Solving inequalities is very similar to solving equations.

First, subtract `color(blue)12` from both sides of the inequality:
`12 + 4x quadcolor(blue)(-quad12) >= 22 quadcolor(blue)(-quad12)`

`4x >= 10`

Now divide both sides by `color(blue)4`:
`(4x)/color(blue)4 > 10/color(blue)4`

`x >= 10/4`

This can still be simplified by dividing both numerator and denominator by `color(blue)2`:
`x >= 10/4 color(blue)(-:2/2)`

`x >= 5/2`

This can also be read as "`x` is greater than or equal to `5/2`".

Hope this helps!