Question

Solve for the variable and graph the solutions:

|2x-4|+110≤120

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for the variable, we can start by subtracting 110 from both sides of the inequality:

|2x-4| ≤ 10

Since the absolute value of a number is always non-negative, we can remove the absolute value brackets:

2x-4 ≤ 10

Now, we can solve for x by adding 4 to both sides:

2x ≤ 14

Dividing both sides by 2:

x ≤ 7

Now, let's consider the other case, where the expression inside the absolute value brackets is negative:

-(2x-4) ≤ 10

Expanding the brackets:

-2x + 4 ≤ 10

Subtracting 4 from both sides:

-2x ≤ 6

Dividing both sides by -2 (and remember that when you do this, you'll need to reverse the inequality sign):

x ≥ -3

Combining the solutions for x:

-3 ≤ x ≤ 7

Next, let's graph the solutions. The graph will be a solid line between -3 and 7, indicating that both endpoints are included in the solution. Now we have:

-3 7
------
------[========]----------------------------

The square brackets indicate that both -3 and 7 are included in the solution.