Question

Solve the inequality and graph the solution set. Write the answer in interval notation. Write your answer in exact simplified form

0> 20x+2>-32

what is the solution?
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Answer 1

The solution is
`\:\left(-(17)/(10),\:-(1)/(10)\right)`.

Explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following:

• ≤, "less than or equal to"
• <, "less than"
• >, "greater than"
• ≥, "greater than or equal to"

To find the solution of the inequality
`0>\:20x+2>\:-32` you must:

`\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32`

First, solve
`0>20x+2`

`\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\(20x)/(20)<(-2)/(20)\\\\\mathrm{Simplify}\\\\x<-(1)/(10)`

Next, solve
`20x+2>-32`

`20x+2-2>-32-2\\\\20x>-34\\\\(20x)/(20)>(-34)/(20)\\\\x>-(17)/(10)`

Finally, combine the intervals

`x<-(1)/(10)\quad \mathrm{and}\quad \:x>-(17)/(10)\\\\-(17)/(10)<x<-(1)/(10)`

The interval notation is
`\:\left(-(17)/(10),\:-(1)/(10)\right)` and the graph is: