Solve the following inequality. -10<2x-5<3?

Question

Draw a number line to represent your solution. Write the interval notation to represent your solution

Answer 1

- 10 < 2x - 5 < 3

add 5 to all three

- 5 < 2x < 8

divide by 2

- 5/2 < x < 4

<------o========o------>
.......-5/2................4
(= is the shaded area)

Answer 2

2x - 5 < 3
2x < 8
x < 4
2x - 5 > -10
2x > - 5
x > - 5/2
- 5/2 < x < 4
{x : - 5/2 < x < 4}

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5
--------------o________o----------

Solid line on above number line represents solution.Circles at -5/2 and 4 are not included in solution.(difficult to draw)

Answer 3

-(5/2)>x>4

Answer 4

-10<2x-5
+5 on both sides
-5<2x
divide 2 on both sides
-2.5
that's one solution

2x-5<3
+5 on both sides
2x<8
divide 2 on both sides
x<4

that's the other solution

on the number line, you draw a horizontal line and but two arrow marks on the ends of it to show that the line goes on forever and there are more numbers.

I don't know about you, but my teacher allowed me to just put two slash marks and but my x= solutions there...you could do that

after that put two not-filled-in- circles on the slash marks

and shade it according to your solutions
so you would shade the line right of -2.5 and left of 8.
and ta-daaa there you go

DO NOT shade the circles

Answer 5

-10<2x-5<3

1. -10+5<2x<3+5
2. -5<2x<8
3. -2.5

Answer 6

1. -10+5<2x-5+5<3+5
2. -5<2x<8
3. -5/2<2x/2<8/2
4. -2.5 <----------(-2.5)<========>(4)-------------->


<=========> those are the areas that are shaded

Answer 7

Add 5 from both sides:
-5<2x<8
-5/2
<------(-5/2)========4-------->

(-5/2,4)

Answer 8

Pathetic that you can't follow along with class notes or text book example.

Answer 9

x=(-5/2,1)