algebra help?

Question

can someone explain how to get answers for there problems?

whats the x-intercept for the line y= -5x-9?

find all solutions to the equation l7x+4l =18

factor the polynomial x^2-5x-36

and solving x^2-9x=36

Answer 1

X-intercept means where the line crosses the x-axis. The x-axis is where y equals 0. So, plug in 0 for y and you will find the x-intercept.
0 = -5x - 9
5x = -9
x = -9/5
Write it as a coordinate: (-9.5, 0)
---------------------------------
|7x + 4| = 18

Split this into two equations and solve. The reason is because what's inside the absolute value signs could be either positive or negative. So, you have to accommodate for that.

7x + 4 = 18
7x = 14
x = 2

-(7x + 4) = 18
-7x - 4 = 18
-7x = 22
x = -22/7
----------------------------
x^2 - 5x - 36

Your answer should be able to be FOILed to get back to this. Find two numbers that multiply to get 36 and add to get 5. Then choose your signs wisely.

(x + 4)(x - 9)
----------------------------
x^2 - 9x = 36

x^2 - 9x - 36 = 0
(x + 3)(x - 12) = 0
x = -3 or 12

Answer 2

whats the x-intercept for the line y= -5x-9?
Just set y= 0 and find x. -5x=9 --> x = -9/5

find all solutions to the equation l7x+4l =18
7x+4 = 18 --> 7x = 14 --> x=2
7x+4 = -18 --> 7x = -22 --> x = -22/7

factor the polynomial x^2-5x-36
(x-9)(x+4)

and solving x^2-9x=36
x^2-9x -36 = 0
(x-12)(x+3)=0
x = 12
x = -3

Answer 3

y = - 5x - 9
intercept = -9
slope = -5

I 7x +4 I = 18
take the positive
7x + 4 = 18
7x = 14
x = 2
take the negative
7x + 4 = - 18
7x = - 22
x = - 22 / 7

factor x^2 - 5x - 36
( x + 4 ) ( x - 9)

solve x^2 - 9x - 36 = 0
(x+3)(x - 12) = 0
x = - 3 . . . and . . x = 12