Confused About This Problem

[ImagineDragons]

What is the minimum value of x for this inequality?

4x + 3( x - 1/5) ≥ 1/5( 2 + x )

[Buenchico]

Typing equations (and inequalities) in a way which is clear to others online can be an absolute nightmare.

When it's written out by hand, does the fraction line in the first bracket pass under the whole of 'x -1'? (Or does the bracket simply contain 'x - one fifth'?)

Also, does the right-hand-side have a numerator of '1' and a denominator of '5(2 + x)'? (Or is the right-hand simply one fifth of '2 + x'?)

[fiction-factory]

I agree with Buenchico of course.
Whatever the exact terms are, you need to multiply each bracket by the term outside and then collect like terms.
So, assuming yours is exactly as written you would have
4x +3x - 3/5 ≥ 2/5 +x/5
then collect like terms:
7x - 3/5 ≥ x/5 +2/5
then rearrange, by doing the same to both sides of the equality
34x/5 ≥ 1
so 34x ≥5

I'll let you do the last step.

If it's written incorrectly and the terms are algebraic fractions so you have terms involving x as denominators then it's trickier to rearrange

[bhg481]

I came to exactly the same solution as fiction-factory.

[fiction-factory]

Thanks. I'd have been more comfortable doing this with pen and paper- it's easy to mistype a step on here or slip up. I notice I mistyped inequality as equality

[fiction-factory]

Did you agree with this and finish it off, ImagineDragons?