Solve and graph the possible solutions to the following word problem.

Question

Two more than three times a number is at most negative four or one less than twice a number is more than one.

(1 point)
Responses

Answer 1

Let's solve the two given equations to find the possible solutions:

1) "Two more than three times a number is at most negative four"
Let's represent the number as "x":
3x + 2 ≤ -4

We can solve this inequality by subtracting 2 from both sides:
3x ≤ -6

Then dividing both sides by 3, we find:
x ≤ -2

So, the solution to the first equation is x ≤ -2.

2) "One less than twice a number is more than one"
Again, representing the number as "x":
2x - 1 > 1

Let's solve this inequality by adding 1 to both sides:
2x > 2

Then, dividing both sides by 2:
x > 1

So, the solution to the second equation is x > 1.

Combining both solutions, we have:
x ≤ -2 or x > 1

To graph this solution, we can represent it on a number line:
```
<--(-Inf)=====-2=======1=====(+Inf)-->
```
The shaded region represents the values of x that satisfy the given word problem.