inequalities help

Irish Fox

Need help with these 2 sums

-7 < - x < 2 , x ∈ z

0 ≤ 3 - 4x < 2 , x ∈ r

thanks

Indiego

-7 < - x < 2
-7 < -x
7 > x

-7 < - x < 2
-x < 2
x < -2

Because x ∈ z, x is an integer which is any whole numbers

x is less than 7, but it is also less than -2 so your answer is all numbers less than -2
i.e
x = {... , -4, -3, -2}


0 ≤ 3 - 4x < 2
0 ≤ 3 - 4x
4x ≤ 3
x ≤ 0.75

0 ≤ 3 - 4x < 2
3 - 4x < 2
3 - 2 < 4x
4x > 1
x > 0.25

Because x ∈ r, x is a real number, which basically is any number including decimals and fractions etc.

x is less than or equal to 0.75 and greater than 0.25 so we know that x is 0.75 and all numbers between it and 0.25

x = {0.26, 0.27, 0.28, ... , 0.75}


Hope this made sense

Irish Fox

makes perfect sense thank you very much

Luno

Indiego wrote: »

-7 < - x < 2
-7 < -x
7 < x

See this bit here, I thought when you changed signs across the greater than or less than sign was flipped too?

Indiego

M&S* wrote: »

See this bit here, I thought when you changed signs across the greater than or less than sign was flipped too?

Ah yeah I missed that bit
4th year's making me soft :pac:
Thanks