Is there any math intellectuals out there cause Sorry for bothering anyone but by now I’...

Move all terms not containing z
to the right side of the inequality.

First divide by 2 on both sides for the first equation and you are left with:

2.9z+3.5 < 15.1

Then subtract 3.5 onto both sides, so:

2.9z + 3.5 -3.5 < 15.1 - 3.5

This will help get rid of your constant that is connected to the z, because remember we are trying to isolate the z. The only way to isolate a variable in an expression is to move everything but that variable to one side by doing the opposite of what is show. SO if you originally have an addition of the variable with a constant (ex. x +3.5 = 0) then you do the opposite to both sides of the equation to get rid of it being associated with the variable.

You are then left with:

2.9z < 11.6

Lastly divide the 2.9 onto both sides and you are left with:

z < 4

In interval notation it is written as (- ∞, -4 )

Both in parentheses due to it being a less than rather than a less than or equal to inequality sign.

You can solve the second equation by doing similar steps. First divide by 4 to both sides, then minus the constant to both sides. Once you minus the constant over, you must simplify it by finding a common denominator and combining the fraction. Once this is done you can then divide the value that is multiplied with the variable to both sides.

4(1.5z+1.25)_>-7.0

1.5z+1.25 _> -7.0/4

1.5z _> (-7.0/4) - 1.25

To get a common denominator so that you can simplify the values on the right side of the equation, you first multiply the -1.25 by 4 on both the top and bottom of it. I say this as -1.25 can also be written in fraction form as (-1.25/1)

So both the -1.25 and the 1 get multiplied by 4.

See as such:

1.5z _> (-7.0/4) - (1.25/1)(4/4)

This gives us a common denominator, as seen next:

1.5z _> (-7.0/4) - (5/4)

We can then combine the right side, take note that with common denominators, when combining, you keep the same value and only simplify the top portion. Can be rewritten as this:

1.5z _> (-7.0 - 5)/4

Now simplify it.

1.5z _> -12/4

Can further simplify:

1.5z _> -3

Last step is to divide both sides by 1.5.

z _> -3/1.5

z _> -2

This written in interval notation is:

[-2 , ∞ )

Notice that the -2 has a bracket, this is due to it being a greater than or equal to -2.

That being said, only the second equation, which has an interval of [-2 , ∞ ) can have a solution of 1 given that 1 falls within the interval.

The first equation is not the answer as the interval is (- ∞, -4 ) and the value 1 does not fall within this interval.

Hope this helped!

edit to my post, both has a solution of 1. I realized I accidently added a negative to the 4 from the first equation. The correct interval should be (- ∞, 4 ) or z < 4

Omfg I appreciate you so much even tho u weren't helping me-

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thank you such a livesaverᶘ ᵒᴥᵒᶅ