How to solve the following for x a x3 2x 9 x 2 b xx2 3 H

How to solve the following for x a. x+3 = -2x + 9 -(x -2) b x(x-2) = -3 , How to use interval notation to express the solution set for 3(x+5) > 5x - 12 also show the solution on a number line , Consider the equation 3x + 2y + 12 = 0 a. Find the slope b. Find the y-intercept c. Suppose that the x-value increases by 2 What is the corresponding change is y?

Solution

a. x+3 = -2x + 9 -(x -2)

x+3 = -2x +9 -x +2

x+3x = 9 +2 -3

4x = 8

x = 4

b) x(x-2) =-3

x^2 -2x +3

It cannot be facttosried:

Use the quadratice formula:

x = (-b +/- sqrt(b^2 -4ac))/2a

x = (2+/- sqrt(4-12))/2

= ( 2+/- 2sqrt2*i)/2

x = 1+ sqrt2*i , 1- sqrt2*i complex roots

c) 3x +2y +12 =0

rewriting: 2y = -3x -12

y = (-3/2)x -6

slope = coefficient of x = -3/2

y intercept : plug x=0 ; y = -6

c) x increase by2: y changes by 2*slope = 2*(-3/2) = -3 ; y decreases by 3

= (2