August 19, 2019, 12:55:16 am

### AuthorTopic: Absolute Value Inequatily  (Read 49 times) Tweet Share

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#### Jefferson

• Forum Regular
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##### Absolute Value Inequatily
« on: August 14, 2019, 10:48:47 pm »
0
Hi,
When solving the inequation

| x + 4 | + | x - 3 |  ≥ 7 using algebra,

I get 3 cases.

Case 1: for x < 4
Solving gives x ≤ 4

Case 2: for -4 ≤ x < 3
Solving gives 7 ≥ 7 (gradient of 1 cancels out, leaving horizontal line)

Case 3: for x ≥ 3
Solving gives x ≥ 3

Therefore, I concluded based on the algebra (with the help of Desmos, which shaded only the following regions) that:
x ≤ 4   OR   x ≥ 3

However, it's obvious that this is true for any x values, evident in the graph itself. The section -4 ≤ x ≤ 3 will be 7 for all values of x, which is something the algebra couldn't show.
How should this result be interpreted in the exam? What explanation can we offer?
Would the answer be "True for all real x"?

Desmos Graph
https://www.desmos.com/calculator/frdjmru5xl

Thank you.
« Last Edit: August 14, 2019, 10:56:04 pm by Jefferson »

#### blyatman

• Trailblazer
• Posts: 25
• Blyat
• Respect: 0
##### Re: Absolute Value Inequatily
« Reply #1 on: August 14, 2019, 11:15:39 pm »
+1
Hi,
When solving the inequation

| x + 4 | + | x - 3 |  ≥ 7 using algebra,

I get 3 cases.

Case 1: for x < 4
Solving gives x ≤ 4

Case 2: for -4 ≤ x < 3
Solving gives 7 ≥ 7 (gradient of 1 cancels out, leaving horizontal line)

Case 3: for x ≥ 3
Solving gives x ≥ 3

Therefore, I concluded based on the algebra (with the help of Desmos, which shaded only the following regions) that:
x ≤ 4   OR   x ≥ 3

However, it's obvious that this is true for any x values, evident in the graph itself. The section -4 ≤ x ≤ 3 will be 7 for all values of x, which is something the algebra couldn't show.
How should this result be interpreted in the exam? What explanation can we offer?
Would the answer be "True for all real x"?

Desmos Graph
https://www.desmos.com/calculator/frdjmru5xl

Thank you.