Solve the Following Inequalities???

Question

Solve the Following Inequalities and then Graph the solution on a number line.


(>_) greater than or equal to
(<_) less than or equal to

A.) abs(2x-8)(>_) 5

I think this is how you do this one...

2x-8(>_) 5
x(>_)6.5

then

2x-8(<_) -5
x(<_)1.5

<-----------------[ (1.5)------------(6.5) ]------>

Now I can't figure out the other two questions...

B) x^2+3x-10(<_)18


C) 5 < 3x+1 (<_) 10

Please help me! Thank you very much!

I need a number line included in the answer. Thank you.

Answer 1

B) x^2 + 3x - 10 (<_) 18
x^2 + 3x (<_)28
i dont know the rest

C) 5 < 3x + 1 , 3x + 1 (<_) 10
4<3x 3(1.3) +1(<_)10
1.3 < x 4.9 (<_)10

For some reason i think that that is wrong

Answer 2

B) x^2 + 3x - 10 (<_) 18
-18 -18 - subtract 18 to make the right side equal 0

x^2 + 3x - 28 (<_) 0
Then you can complete the square
(x - 4)(x + 7) (<_) 0
Then you set both sets of the equations in the parenthecies to 0 and solve.

x - 4 (<_) 0 x+7 (<_) 0
x (<_) 4 x (<_) -7

You could also use the Quadratic Equation and plug in a = 1, b = 3, and c = -28 and solve.

C) **You have to seperate the two inequalities and then solve**

So, you have:
5 < 3x + 1
-1 -1 - subtract 1 from both sides
4 < 3x
/3 /3 - divide both sides by 3

4/3 < x
THEN,
3x + 1 (<_) 10
-1 -1 - subtract 1
3x (<_) 9
/3 /3 - divide 3
x(<_) 3
So, you answer would look like: 4/3 < x (<_) 3

Answer 3

B) factor (x+5)(x-2) (<_)18..... set each one separate x+5(<_)18 and x-2 (<_) 18 and solve for each like you did in A.

C) separate it out 5<3x+1 and 3x+1(<_) 10 solve each one like you did for A.