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

Answer:

The solution is $\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)$.

Step-by-step 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 $0>20x+2$

$\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}$

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

$20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}$

Finally, combine the intervals

$x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}$

The interval notation is $\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)$ and the graph is: