Question

Hi. I need help with this question :

Question : y is such that

`4y - 7 \leqslant 3y` and

`3y \leqslant 5y + 8`:
I). What range of values satisfies both inequalities ?
II). Hence, express

`4y - 7 \leqslant 3y \leqslant 5y + 8`
in the form of

`a \leqslant y \leqslant b`
where a and b are both integers.

Please show workings.

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Answer 1

-4≤y≤7

Explanation:

4y-3y≤7

y≤7

and

3y-5y≤8

-2y≤8

y≥-4

so, -4≤y≤7

Answer 2

9514 1404 393

Answer:

-4 ≤ y ≤ 7

Explanation:

Solve the inequalities separately, then identify the intersection of the solution sets.

4y -7 ≤ 3y

y -7 ≤ 0 . . . . . . . subtract 3y

y ≤ 7 . . . . . . . . . add 7

3y ≤ 5y +8

0 ≤ 2y +8 . . . . . . subtract 3y

-8 ≤ 2y . . . . . . . . . subtract 8

-4 ≤ y . . . . . . . . . . divide by 2

The intersection of the sets y ≤ 7 and -4 ≤ y is given by ...

-4 ≤ y ≤ 7