Question

Find the solution set of each equality if the replacement set for each variable is {-10,-9,-8,...,8,9,10}. 16-19?!

Answer 1

QUESTION 16

The given inequality is
`n-3\geq (n+1)/(2)`.

We first multiply through by the least common multiple, which is
`2` to get,

`2(n-3)\geq (n+1)/(2) * 2`

This simplifies to

`2(n-3)\geq n+1`

We expand brackets to get,

`2n-6\geq n+1`

We group like terms to get,

`2n-n\geq 1+6`

`\Rightarrow n\geq 7`.

We now choose the values from the replacement set

{
`-10,-9,-8,...,8,9,10`}.

The solution set is therefore

{
`7,8,9,10`}

QUESTION 17

We want to solve
`(2(x+2))/(3)\:<\:4`

We multiply through by 3 to get,

`3* (2(x+2))/(3)\:<\:4* 3`

This simplifies to,
`2(x+2)\:<\:12`

We now expand brackets to get,

`2x+4\:<\:12`

We group like terms to get,

`2x\:<\:12-4`

`\Rightarrow 2x\:<\:8`

`\Rightarrow x\:<\:4`

We now choose the values from the replacement set

{
`-10,-9,-8,...,8,9,10`}.

The solution set is therefore

{
`-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3`}

QUESTION 18

We want to solve
`1.3y-12\:<\:0.9y+4`.

We group like terms to get,

`1.3y-0.9y\:<\:4+12`.

We simplify to get,

`0.4y\:<\:16`.

We divide through by 0.4 to get,

`y\:<\:40`.

This time the complete replacement is the solution set of the inequality because all the elements satisfies
`y\:<\:40`.

The solution set is

{
`-10,-9,-8,...,8,9,10`}

QUESTION 19

We want to solve
`-20\geq 8+7k`.

We group like terms to get,

`-20-8\geq 7k`

This implies that,

`-28\geq 7k`

We divide through by 7 to get,

`-4\geq k`

We can rewrite this as
`k\leq -4`.

We now choose the values from the replacement set {
`-10,-9,-8,...,8,9,10`}. The solution set is therefore

{
`-10,-9,-8,-7,-6,-5,-4`}