Question

Solve. Write the solution in interval notation. -2x>-8 and -5x<20.

Answer 1

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)