Does anybody know how to do this?? (solving inequalities)?

Question

Solve each inequality and graph the solution set. Also express the solution in interval notation form

6x + 8 is less than 20
5x+4 is less than 29
-3x
-3x+7 is greater than -11
4/5x +6 is greater than 20


ps. best answer goes to the person who can make me understand how to do this .

thanks a lot guys

Answer 1

Solving inequalites are just as simple as solving equalities using simple algebra. The trick is to act as if the inequality is an =, changing dircetion only if mutliplication of a negative occurs.

for example

6X + 8 < 20 becomes
6X <12
X<2

to put this answer into interval notation results in (-infinity, 2)

Get it? the only time it gets tricky is with a negative number multiplied, such as

-3X + 7 > -11
-3X > -18
X < 6 (-inifinity, 6)

If you need more help, IM me.


Ken

Answer 2

We must split this up into their own equations...

(a) 6x + 8 < 20
(b) 5x + 4 < 29
(c) -3x + 7 > -11
(d) (4/5)x + 6 > 20

Just a note in case you are unsure:

Solving inequalities are almost the same as solving normal equations. The trick is to treat the inequality sign the same way you operate with an equal sign. The normal rules still apply. However, if you multiple both sides of an inequality with a negative number, ALWAYS keep in mind that the inequality sign has to CHANGE.

I'll do the first question just to display the basic operations similiar to the "=" sign.

(1) 6x + 8 < 20
(2) 6x < 20 - 8, Subtract 8 from both sides
(3) 6x < 12, Divide both ends by 6
(4) x < 2

Doing each equation and making "x" the subject, you should get the following answers...

(a) x < 2
(b) x < 5
(c) x < 6
(d) x > 11.2

NOTE: For equation (c), both sides have the negative sign. When you remove the negatives, the sign CHANGES. The solution is below if you are still unclear.

(1) -3x + 7 > -11
(2) -(3x - 7) > -11
(3) 3x - 7 < 11, Sign changes when both sides are multiplied by -1
(4) 3x < 18, Divide both ends by 3
(5) x < 6

Thus, the answer is x < 6.

Hope this helps.

Answer 3

Inequalities are solved EXACTLY the same as equations with one exception. Whenever you multiply or divide be a negative number you must remember to change the direction of the inequality symbol. I find it easier to have the variable on the left, too, so if I have it on both sides i would eliminate the one on the right. If there's is only one variable and it's on the right, i would rewrite the inequality before trying to graph it.

Here goes.
1.
6x+8<20 subtract 8 from both sides
6x<12 Divide by 6
x<2

On a number line put an open circle at the number 2 and draw an arrow to the left showing that x is less than two.

Do you mean set notation? {x:x<2}

2.
5x+4<29
5x<25
x<5
Put an open circle at 5 and draw an arrow to the left
{x:x<5}

3.
-3x+7>-11
-3x>-18
x<6 (remember to change the direction of the symbol
Draw an open circle at 6 and an arrow to the left
{x:x<6}

4.
4/5x +6>20
4/5x>14 Multiply by 5
4x>70
x>17.5

Put an open circle at 17.5 and draw the arrow to the right
{x:x>17.5}

Hope I helped.

Answer 4

Inequalities have three simple rules:

1. You can add or subtract the same number to both sides of the inequality.

2. You can multiply or divide both sides of the inequality with a positive number.

3. You can multiply or divide both sides with a negative number, but you have to reverse the inequality. (Less than becomes greater than, and greater than becomes less than)

That's it!

6x+8<20 -> Apply rule 1.
6x+8-8<20-8
6x<12 -> Apply rule 2
6x/6 < 12/6
x<2

-3x+7 > -11 -> Apply rule 1.
-3x+7-7 > -11-7
-3x > -18 -> Apply rule 3
-3x / (-3) < -18 / (-3)
x < 6


Hope this helps

Answer 5

6x+8<20
6x>20-8
6x>12
x>12/6
therefore x>6

the less than or greater than sign is the same as (=)
You keep the letters on the left of the = and the numbers on the right.
When you move the numbers to the other side of the less than sign. It changes to a greater than sign. Also the sign of the number changes when it is mooved too
It's pretty easy after that.
You just subtract and divide by the number on the letter

5x+4<29-3x
5x+3x>29-4
8x>25
x>25/8


-3x+7>-11
-3x<-11-7
-3x<-18
x<18/3

Answer 6

6x + 8 < 20
6x < 12
x < 2

5x + 4 < 29
5x < 25
x < 5
Is that what you mean to say.

Answer 7

infinite