Solve the inequality and express your answer in interval notation

The number line graph is also attached below.

Step-by-step explanation:

Given the inequality

Let's find the critical points of the inequality.

       (Multiply both sides by x-3)

   (Factor left side of equation)

or    (Set factors equal to 0)

or

Check possible critical points.

x = 5  (Works in original equation)

x = −6  (Works in original equation)

Critical points:

x = 5 or x = −6      (Makes both sides equal)

x = 3          (Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x ≤ −6     (Doesn't work in original inequality)

−6 ≤ x < 3      (Works in original inequality)

3 < x ≤ 5         (Doesn't work in original inequality)

x ≥ 5 (Works in original inequality)

so

Therefore,

The number line graph is also attached below.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer: i don't understand. what are the options

step-by-step explanation: