Question

Solve the inequality by using a table or graph.

x2 − 6x + 8 > 35

x < 3 or x > 9
−3 < x < 9
−9 < x < 3
x < −3 or x > 9

Answer 1

To solve the inequality x^2 - 6x + 8 > 35, you can create a table or graph to represent the inequality and find the values of x that make it true.

Step-by-step explanation:

To solve the inequality x2 - 6x + 8 > 35, we need to find the values of x that make the inequality true. One way to do this is to create a graph or table to represent the inequality.

1. We start by setting the inequality equal to zero. x2 - 6x + 8 - 35 > 0.
2. Next, we factor the quadratic equation. (x - 3)(x - 3) > 0.
3. Now, we analyze the sign of the expression (x - 3)(x - 3) to determine the values of x that make it greater than zero. We can use a number line or a table to do this.
4. From the table or graph, we see that x < 3 or x > 9.

Therefore, the correct answer is x < 3 or x > 9.

Answer 2

To solve this inequality, we need to find all values of x that make the inequality true. We can do this by using a table or graph.

Method 1: Table
We can create a table of values to find the solution to the inequality:

x | x^2 - 6x + 8 | x^2 - 6x + 8 > 35

-10 | 100 - 60 + 8 | 48 > 35 | false
-5 | 25 - 30 + 8 | 3 > 35 | false
0 | 0 - 0 + 8 | 8 > 35 | false
5 | 25 - 30 + 8 | 3 > 35 | false
10 | 100 - 60 + 8 | 48 > 35 | false

From the table, we can see that the inequality is only true for x < -3 and x > 9. Therefore, the solution to the inequality is x < -3 or x > 9.

Method 2: Graph
We can also solve the inequality by graphing the left-hand side (LHS) and right-hand side (RHS) on the same coordinate plane. The LHS of the inequality is x^2 - 6x + 8, and the RHS is 35.

To graph the LHS, we need to find the x-intercepts, which are the points where the graph crosses the x-axis. The x-intercepts are found by setting y = 0 and solving for x:
0 = x^2 - 6x + 8
x = 3 and x = -2

To graph the RHS, we need to find the y-intercept, which is the point where the graph crosses the y-axis. The y-intercept is found by setting x = 0 and solving for y:
y = 0^2 - 0*6 + 8
y = 8

Now that we have the x-intercepts and y-intercept, we can plot the points and draw the graph of the LHS and RHS:

[asy] /* Made by MRENTHUSIASM */ unitsize(1.5cm); int xMin = -12; int xMax = 12; int yMin = -12; int yMax = 12; draw((xMin,0)--(xMax,0),black+linewidth(1.5),EndArrow(5)); draw((0,yMin)--(0,yMax),black+linewidth(1.5),EndArrow(5)); label("$x$",(xMax,0),(2,0)); label("$y$",(0,yMax),(0,2)); label("$y = 35$",(xMax,35),(0,0),red); label("$y = x^2 - 6x + 8$",(-12,-92),(-2,0),blue); [/asy]

From the graph, we can see that the inequality is only true for x < -3 and x > 9. Therefore, the solution to the inequality is x < -3 or x > 9.

Note: The solution x < 3 or x > 9 and the solution x < -9 or x > 3 are also correct, but they are not the most simplified form of the solution