Question

How would I graph this inequality?

`7x+3y\ \textless \ 6-5x`

Answer 1

the graph in the attached figure

Explanation:

we have

`7x+3y<6-5x`

isolate the variable y

Subtract 7x both sides

`3y<6-5x-7x`

`3y<-12x+6`

Divide by 3 both sides

`y<-4x+2`

The solution of the inequality is the shaded area below the dashed line

The equation of the shaded line is
`y=-4x+2`

The slope of the dashed line is negative
`m=-4`

The y-intercept of the dashed line is the point
`(0,2)`

The x-intercept of the dashed line is the point
`(0.5,0)`

To graph the inequality plot the intercepts and shade the area below the dashed line

using a graphing tool

the graph in the attached figure