Question

{x: –1≤x – 2 ≤7} what doe sthis means ? just need an explaination and way to do it

Answer 1

" : "can be prononunce as such that so we can say it like this that value of x such that x-2 belongs from -1 to 7

-1<x-2<7

on adding 2 in this inequality

-1+2<x-2+2<7+2

therefore x belongs to [1,9] or 1<x<9

Answer 2

-1≤x -2 ≤ 7

This means that x -2 is greater than or equal -1 (-1 ≤ x-2) and 7 is greater or equal to x-2. These type of equations are known as inequalities.

you have to solve it by separating it into parts.

1. -1≤ x-2

by transposing -2

-1+2≤ x

1 ≤ x ......(1)

2. x-2≤7

by transposing -2

x ≤ 7+2

x≤ 9 ....(2)

» We get,

1≤ x , x≤ 9

it means that x should be greater or equal to 1 and x should be equal to or smaller than 9.

so, x = {1,2,3....9}

so we can write that,

${\pink{\boxed{x \in[1,9] \ or\ 1\leqslant x \leqslant 9}}}$ (combined form of equations 1 and 2)