Question

Solve the two step inequality and match the answer to the graph.

Answer 1

SOLVING THE INEQUALITY
`3x-10<-25` TO MATCH OPTION A

Considering the inequality

`3x-10<-25`

`3x-10+10<-25+10`

`3x<-15`

`(3x)/(3)<(-15)/(3)`

`x<-5`

Thus,

`3x-10<-25\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-5\right)\end{bmatrix}`

Therefore, the inequality
`3x-10<-25` has the solution
`x<-5` which matches the option A.

SOLVING THE INEQUALITY
`-4x+7\ge \:27` TO MATCH OPTION B

Considering the inequality

`-4x+7\ge \:27`

`-4x+7-7\ge \:27-7`

`-4x\ge \:20`

`\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}`

`\left(-4x\right)\left(-1\right)\le \:20\left(-1\right)`

`4x\le \:-20`

`(4x)/(4)\le (-20)/(4)`

`x\le \:-5`

Thus,

`-4x+7\ge \:27\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-5\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-5]\end{bmatrix}`

Therefore, the inequality
`-4x+7\ge \:27` has the solution
`x\le \:-5` which matches the option B.

SOLVING THE INEQUALITY
`(x)/(1)-9<-10` TO MATCH OPTION C

Considering the inequality

`(x)/(1)-9<-10`

`\mathrm{Apply\:rule}\:(a)/(1)=a`

`x-9<-10` ∵
`(x)/(1)=x`

`x-9<-10`

`x-9+9<-10+9`

`x<-1`

`(x)/(1)-9<-10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\end{bmatrix}`

Therefore, the inequality
`(x)/(1)-9<-10` has the solution
`x<-1` which matches the option C.

SOLVING THE INEQUALITY
`5\left(x-2\right)>-15` TO MATCH OPTION D

Considering the inequality

`5\left(x-2\right)>-15`

`\mathrm{Divide\:both\:sides\:by\:}5`

`(5\left(x-2\right))/(5)>(-15)/(5)`

`x-2>-3`

`x-2+2>-3+2`

`x>-1`

Thus,

`5\left(x-2\right)>-15\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-1,\:\infty \:\right)\end{bmatrix}`

Therefore, the inequality
`5\left(x-2\right)>-15` has the solution
`x>-1` which matches the option D.