Can anyone show me how to do these problems step by step please? (I wanna learn)?

Question

Solve each inequailty. Graph the solution set. (No calcuators please) I wanna learn the old way

1. 2t - 9 < 21

2. 5x + 4 >or equal to 34

3. 6s - 7 < 29

4. 15- 2t >or equal to 55

5. 5(x - 3) >or equal to 15

6. -4(13 - 6t) < 26

Answer 1

I don't have time to do all of them, but I'll do number one for you, and then maybe the next person can do number two, etc...

2t-9<21 Add 9 to both sides
2t<30 Divide both sides by 2
t<15

Answer 2

You can treat inequalities almost like regular equations. The only thing to be aware of is that the inequality sign changes direction ( > becomes <, and < becomes > ) when you multiply or divide by a negative number.

so let's get started:
1. 2t - 9 < 21

2t - 9 < 21
add 9 to both sides
2t < 30
divide by +2
t < 15
the sign stays the same because you are dividing by a positive number

2. 5x + 4 >= 34

5x + 4 >= 34
subtract 4 from both sides
5x >= 30
divide both sides by +5
x>=6

3. 6s - 7 < 29

6s - 7 < 29
6s < 36
s< 6

4. 15 - 2t >= 55

15 - 2t >= 55
subtract 15 from both sides
-2t >= 40

note the negative sign above
To get t by itself, you need to divide by -2
but when you divide or multiply by a negative number, you need to switch the direction of the inequality sign, so we have:

t =< -20
the equals sign part stays the same because equals just stays equals

5. 5(x - 3) >= 15

5(x - 3) >= 15
distribute the 5 to get
5x - 15 >= 15
5x >= 30
x>= 6

6. -4(13 - 6t) < 26

-4(13 - 6t) < 26
distribute the -4 to get
-52 + 24t < 26
you don't need to change the inequality sign because you are only distributing the -4 over one side, and not multiplyiing BOTH sides by the negative number
Now add 52 to both sides to get
24t < 78
t < (78/24)
t < (13/4)
t < 3.25

I hope that helps you!

Answer 3

you already have 1 & 2...

3. 6s - 7 < 29
6s < 36
s < 6

4. 15 - 2t >= 55
-2t >= 40
t <= -20 *when multiplying.dividing by a negative, switch the sign!

5. 5(x-3) >= 15
5x - 15 >= 15
5x >= 30
x >= 6

6. -4(13 - 6t) < 26
-52 + 24t < 26
24t < 78
t < 3.25

oh, to graph the solution set, mark the number with an open circle for normal ones or a closed circle for those that have an "or equal" in them, then shade in the region that is more or less than that number, depending what the solution says

...sorry I got 4 wrong, I fixed it now.

Answer 4

1. 2t - 9 < 21
2t -9 + 9 < 21 + 9
2t < 30
2t/2 < 30/2
t < 15
2. 5x + 4 >/= 34
5x >/= 34 - 4
5x >/= 30
5 >/= 6

3. 6s - 7 < 29
6s - 7 + 7 < 29 +7
6s < 36
6s/6 < 36/6
s < 6

4. 15 - 2t >= 55
- 2t >= 55-15
-2t >= 40
-2t/-2 >= 40/-2
t <= -20

5. 5(x-3) >= 15
5x - 15 >= 15
5x >= 30
x >= 6

6. -4(13 - 6t) < 26
-52 + 24t < 26
24t < 78
t < 13/4
solved

Answer 5

1.
2t - 9 < 21 Combine constants on Right Hand Side
2t < 12 Divide out 2 from both sides
t < 6

2.
5x + 4 >= 34 Combine the constants on the Right Hand Side
5x >= 30 Divide out 5 from both sides
x > = 6

3.
6s - 7 < 29 Start the same way. Combine the constants
6s < 36 Divide out the factor on you variable (6)
s < 6

4.
15 - 2t >= 55 Start out the same way. -15 both sides
-2t >= 40 Divide out the -2.. Here is something to pay attention to . WHEN YOU DIVIDE BY A NEGATIVE NUMBER WITH <> SIGNS THEY FLIP....
t <= 20

You can now do 5 and 6. Check your answers below


5. 5x-15 >= 15 -----> x >= 6
6. -52 + 24 t < 26 ------> t < 78/24

Answer 6

basically you just pretend the inequality is an = sign and solve it like a normal equation, but you reverse the sign if you divide your variable by a negative number. I'll demonstrate with #1 and #4.
1. 2t-9 < 21
2t < 21+ 9
2t < 30
t < 30/2
t< 15

4. 15-2t >= 55
-2t >= 55 -15
-2t >= 40
t<= 40/-2 (note reverse of inequality)
t<= -20

Answer 7

You basically pretend it's an equation. Like for number 1, you'd add 9 to both sides and get 2t<30, then divide both sides by 2 so you get t<15. Then to graph it you simply draw and label a number line up to 30 (using increments of 10 would probably be easiest). Draw an open circle on 30 (to indicate that t does not equal 30) and an arrow going to the left toward 0. For the problems where x > or equal to whatever, you draw a filled in circle on whatever number, to indicate that x does equal that number.
Good luck!

Answer 8

1. 2t - 9 < 21
2t < 21 + 9
2t < 30
t < 15
2. 5x + 4 >/= 34
5x >/= 34 - 4
5x >/= 30
5 >/= 6

Just follow as the same way..good luck

Answer 9

im not gunna do ur homework :P

treat the inequality as an equation (ignore the inequality)

IMPORTANT RULE:
if dividing by a negative number, reverse the inequality sign

Gary G you forgot to divide 9 by 2 ;)

Answer 10

i think thats right you need to get rid of the number in front of the letter then u must get the letter to one side buy itself