Answer:
The interval notation of the solution is (-4 , 4)
Step-by-step explanation:
* Let us explain a very important point in solving inequality
- When you multiply or divide an inequality by negative number we
must reverse the symbol of the inequality
- Ex:
∵ 2 < 3
- If we multiply the both sides of the inequality by -1, then the
inequality will be -2 < -3 and this is completely wrong, so we must
reverse the symbol of the inequality
∴ -2 > -3
* Now let us solve the problem
∵ -2x > -8
- Divide both sides by -2 and remember to reverse the symbol of the
inequality
∴ x < 4
∵ -5x < 20
- Divide both sides by -5 and remember to reverse the symbol of the
inequality
∴ x > -4
- From both solutions
∴ -4 < x < 4
∴ The solution is {x : -4 < x < 4}
- Interval notation is a way of writing the solutions of inequalities
( , ) if x does not equal the end numbers
[ , ] if x equals the end numbers
[ , ) , ( , ] if x equals one of the two end numbers
* The interval notation of the solution is (-4 , 4)
lies between the two consecutive numbers 3 and 4. 