Question

Solve the inequality (question 30 please, already solved others)

Answer 1

n ≤ 32

Explanation:

Given

`(1)/(4)` n + 12 ≥
`(3)/(4)` n - 4

Subtract
`(1)/(4)` n from both sides

12 ≥
`(1)/(2)` n - 4 ( add 4 to both sides )

16 ≥
`(1)/(2)` n ( multiply both sides by 2 )

32 ≥ n, hence

n ≤ 32

Answer 2

`\bf \cfrac{1}{4}n+12 \geqslant \cfrac{3}{4}n-4\implies \cfrac{1}{4}n+16 \geqslant \cfrac{3}{4}n\implies 16\geqslant \cfrac{3n}{4}-\cfrac{1n}{4}\implies 16\geqslant \cfrac{3n-1n}{4} \\\\\\ 16\geqslant\cfrac{2n}{4}\implies 16\geqslant \cfrac{n}{2}\implies 32 \geqslant n`