Question

How do you solve and graph this inequality? 4x-3≥-1

I really don't understand how to graph it! Help!!!!

Answer 1

The solution to the inequality expression `color(blue)(4x-3>= (-1)` is `color(green)(x>=1/2`.

Explanation:

Given:

Inequality expression `4x-3>= (-1)`

Objective:

Keep `color(red)x` on one side and all the other numeric values on the other side of the inequality.

`color(red)("Step 1"`

Add `3` to both sides of the inequality.

`4x-3+color(red)( 3)>= (-1)+color(red) 3`

`4x-cancel 3+cancel 3 >=2`

`rArr 4x>=2`

`color(red)("Step 2"`

Divide both sides of the inequality by `color(red)4`

`rArr (4x)/color(red)4>=2/color(red) 4`

`rArr x>=1/2`

`rArr x>=0.5`

Hence,

the solution to the inequality expression `color(blue)(4x-3>= (-1)` is `color(green)(x>=1/2` OR `color(green)( x>= 0.5`.

`color(red)("Step 3"`

Inequality graph is below:

Hope you find this solution helpful.