# -4 < 5-3x < 20 find x values

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The correct answer to this is that x is greater than -5 and that x is less than 3. You can find this answer in the following way.

Remember that you can solve this inequality just as you would solve any other equation.

First, subtract 5 from all sides of the equation. Now you have

-9 < -3x < 15

Now, divide all sides of the equation by -3. Be sure to change the directions of the signs. You have to do this whenever you multiply or divide by a negative number. Now you have

3 > x > -5

-4 < 5-3x < 20

We will sove it just like we solve any equation:

First subtract 5 from ALL sides:

==> -4-5 < 5-3x -5 < 20-5

==> -9 < -3x < 15

Now divide by (-3)

(Notice that when multiplying or dividing by a negative number, we need to reverse the inequality or change its dierection.

==> -9/-3 > -3x/-3 > 15/-3

==> 3 > x > -5

Then x belongs to the interval (-5,3)

We'll solve the system of the inequalities in this way:

-4 < 5-3x (1)

5-3x < 20 (2)

We'll solve the first inequality, by isolating to one side the unknown. For this reason, we'll subtract 5 both sides:

-4-5<-5+5-3x

-9<-3x

We'll divide by -3, changing the direction of the inequality:

x<3

We'll solve now the inequality (2):

5-3x < 20 (2)

We'll subtract 5 both sides:

5-5-3x<20-5

-3x<15

We'll divide by -3, changing the direction of the inequality:

x>-5

So, for the double inequality to hold, x has to have values in the interval (-5,3).

We go step by step.

An equation or inequality does not get affected by adding or subtracting equals. So subtract 5.

-4 -5 < 5-3x-5 < 20 -5

-3 < -3x < 15.

An equation or inequality is not affected by multiplying both sides by a positive equal quantity. So Multiply by (1/3).

-3(1/3) < -3x(1/3) < 15(1/3)

-1 < -x < 5.

(An equation is not affected) but an inequality is affected by multiplying both sides by a negative (equal) quantity. The inequality reverses when we multiply both sides by a negative equal quantity. So multiply by -1 both sides and reverse the inequality.

**-1(-1) > -x(-1) > 5(-1)**

1 > x > -5 .

-5 <x < 1.